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G.F. Nane
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1
From Detection to Prevention
Integrating Testing and Vaccination for Measles Control
This thesis investigates how testing information can inform targeted measles vaccination strategies under a limited vaccine supply. We focus on vaccine strategies that allocate vaccine doses to locations flagged as outbreaks. The detection of outbreaks depends on testing information rather than perfect knowledge of true infection status. Because testing capacity is limited, results are delayed, and tests have imperfect sensitivity and specificity, the information obtained from tests is imperfect. We evaluate the benefits and limits of such testing information, and develop a heuristic that integrates testing information in targeted vaccine strategies.
The problem is formulated as an optimal control framework that captures both disease transmission and testing dynamics. Our analyses demonstrate that the optimal solution allocates the entire available vaccine stock to the location(s) where vaccination achieves the greatest reduction in infections. We numerically evaluate our findings using measles data in Senegal. Under homogeneous testing parameters, testing information finds the global optimal allocation, because vaccination’s effect on reducing positive diagnoses is captured regardless of test imperfection. When testing parameters are heterogeneous across locations, testing information may lead to a suboptimal allocation.
While mathematically optimal, the allocation structure risks neglecting locations at risk and therefore may not be fair. To address these concerns, we propose an implementable heuristic that offers a more equitable allocation while still considering the minimization of cumulative infections. The heuristic allocates vaccines to locations where the number of positive diagnoses exceed a threshold, set to the expected number of false positives in an infection-free scenario. This construction ensures that locations without an active outbreak do not exceed the threshold, whereas locations experiencing an outbreak do. We prove that this threshold is optimal when only one location contains infected individuals.
We evaluate the proposed heuristic for a case study of measles transmission in Senegal, providing empirical validation of the theoretical results. We find that targeted vaccination yields the largest reduction in infection, and that among testing parameters, testing capacity decreases health burden the most. ...
The problem is formulated as an optimal control framework that captures both disease transmission and testing dynamics. Our analyses demonstrate that the optimal solution allocates the entire available vaccine stock to the location(s) where vaccination achieves the greatest reduction in infections. We numerically evaluate our findings using measles data in Senegal. Under homogeneous testing parameters, testing information finds the global optimal allocation, because vaccination’s effect on reducing positive diagnoses is captured regardless of test imperfection. When testing parameters are heterogeneous across locations, testing information may lead to a suboptimal allocation.
While mathematically optimal, the allocation structure risks neglecting locations at risk and therefore may not be fair. To address these concerns, we propose an implementable heuristic that offers a more equitable allocation while still considering the minimization of cumulative infections. The heuristic allocates vaccines to locations where the number of positive diagnoses exceed a threshold, set to the expected number of false positives in an infection-free scenario. This construction ensures that locations without an active outbreak do not exceed the threshold, whereas locations experiencing an outbreak do. We prove that this threshold is optimal when only one location contains infected individuals.
We evaluate the proposed heuristic for a case study of measles transmission in Senegal, providing empirical validation of the theoretical results. We find that targeted vaccination yields the largest reduction in infection, and that among testing parameters, testing capacity decreases health burden the most. ...
This thesis investigates how testing information can inform targeted measles vaccination strategies under a limited vaccine supply. We focus on vaccine strategies that allocate vaccine doses to locations flagged as outbreaks. The detection of outbreaks depends on testing information rather than perfect knowledge of true infection status. Because testing capacity is limited, results are delayed, and tests have imperfect sensitivity and specificity, the information obtained from tests is imperfect. We evaluate the benefits and limits of such testing information, and develop a heuristic that integrates testing information in targeted vaccine strategies.
The problem is formulated as an optimal control framework that captures both disease transmission and testing dynamics. Our analyses demonstrate that the optimal solution allocates the entire available vaccine stock to the location(s) where vaccination achieves the greatest reduction in infections. We numerically evaluate our findings using measles data in Senegal. Under homogeneous testing parameters, testing information finds the global optimal allocation, because vaccination’s effect on reducing positive diagnoses is captured regardless of test imperfection. When testing parameters are heterogeneous across locations, testing information may lead to a suboptimal allocation.
While mathematically optimal, the allocation structure risks neglecting locations at risk and therefore may not be fair. To address these concerns, we propose an implementable heuristic that offers a more equitable allocation while still considering the minimization of cumulative infections. The heuristic allocates vaccines to locations where the number of positive diagnoses exceed a threshold, set to the expected number of false positives in an infection-free scenario. This construction ensures that locations without an active outbreak do not exceed the threshold, whereas locations experiencing an outbreak do. We prove that this threshold is optimal when only one location contains infected individuals.
We evaluate the proposed heuristic for a case study of measles transmission in Senegal, providing empirical validation of the theoretical results. We find that targeted vaccination yields the largest reduction in infection, and that among testing parameters, testing capacity decreases health burden the most.
The problem is formulated as an optimal control framework that captures both disease transmission and testing dynamics. Our analyses demonstrate that the optimal solution allocates the entire available vaccine stock to the location(s) where vaccination achieves the greatest reduction in infections. We numerically evaluate our findings using measles data in Senegal. Under homogeneous testing parameters, testing information finds the global optimal allocation, because vaccination’s effect on reducing positive diagnoses is captured regardless of test imperfection. When testing parameters are heterogeneous across locations, testing information may lead to a suboptimal allocation.
While mathematically optimal, the allocation structure risks neglecting locations at risk and therefore may not be fair. To address these concerns, we propose an implementable heuristic that offers a more equitable allocation while still considering the minimization of cumulative infections. The heuristic allocates vaccines to locations where the number of positive diagnoses exceed a threshold, set to the expected number of false positives in an infection-free scenario. This construction ensures that locations without an active outbreak do not exceed the threshold, whereas locations experiencing an outbreak do. We prove that this threshold is optimal when only one location contains infected individuals.
We evaluate the proposed heuristic for a case study of measles transmission in Senegal, providing empirical validation of the theoretical results. We find that targeted vaccination yields the largest reduction in infection, and that among testing parameters, testing capacity decreases health burden the most.
Copulas are useful for studying how several random variables depend on each other, because they allow the dependence structure to be separated from the individual marginal distributions. This makes them particularly useful when the main interest is in whether the dependence itself changes over time. In this thesis, I study this problem for a multivariate time series whose dependence is described by a copula from a fixed parametric family. The main goal is to test whether the copula parameter remains constant over the whole sample or changes once at an unknown point in time. For each possible change-point, a model with one common copula parameter is compared with a model that allows different parameters before and after the split. Since the change location is unknown, the final test statistic is obtained by taking the largest value over a trimmed set of candidate change-points.
I first consider the ideal case, where the marginal distributions are known. In this setting, the true copula observations are available directly. The main difficulty is that the test does not use only one fixed split point, but searches over many possible locations. Therefore, the likelihood approximations need to hold uniformly over all candidate change-points. To do this, I first control the score process and the observed information matrices uniformly over the candidate splits. These results are then used to describe the estimation errors of the maximum likelihood estimators. From there, the likelihood ratio statistic can be rewritten as a quadratic form involving a centered score process. This process converges to a standard multivariate Brownian bridge, which gives the limiting distribution of the maximized test statistic.
The feasible case is more difficult because the marginal distributions are unknown. The true copula observations are then replaced by rank-based pseudo-observations. For every possible change-point, the ranks are recomputed separately in the two resulting segments. Because of this, the score terms are no longer simple partial sums of independent observations. To handle this, I use the sequential localrank empirical copula process and combine it with a function-indexed integration-by-parts argument. This makes it possible to derive the weak limit of the local-rank score process and, from this, the limiting distribution of the feasible likelihood ratio statistic. The resulting limit still has a Brownian-bridge-type structure, but its covariance also reflects the additional effect of estimating the marginal distributions through ranks.
Finally, I study the finite-sample behaviour of the test through simulations using Gaussian and Student 𝑡 copulas. The results show a clear general pattern: the test becomes more powerful when the sample size increases or when the change in dependence becomes larger. Small changes are harder to detect, especially for the feasible procedure based on local ranks. At the same time, the difference between the ideal and feasible procedures becomes smaller for larger samples and stronger changes in dependence. Overall, the thesis develops the theoretical justification for a likelihood-ratio change-point test in copula models and studies how the procedure behaves in finite samples.
...
I first consider the ideal case, where the marginal distributions are known. In this setting, the true copula observations are available directly. The main difficulty is that the test does not use only one fixed split point, but searches over many possible locations. Therefore, the likelihood approximations need to hold uniformly over all candidate change-points. To do this, I first control the score process and the observed information matrices uniformly over the candidate splits. These results are then used to describe the estimation errors of the maximum likelihood estimators. From there, the likelihood ratio statistic can be rewritten as a quadratic form involving a centered score process. This process converges to a standard multivariate Brownian bridge, which gives the limiting distribution of the maximized test statistic.
The feasible case is more difficult because the marginal distributions are unknown. The true copula observations are then replaced by rank-based pseudo-observations. For every possible change-point, the ranks are recomputed separately in the two resulting segments. Because of this, the score terms are no longer simple partial sums of independent observations. To handle this, I use the sequential localrank empirical copula process and combine it with a function-indexed integration-by-parts argument. This makes it possible to derive the weak limit of the local-rank score process and, from this, the limiting distribution of the feasible likelihood ratio statistic. The resulting limit still has a Brownian-bridge-type structure, but its covariance also reflects the additional effect of estimating the marginal distributions through ranks.
Finally, I study the finite-sample behaviour of the test through simulations using Gaussian and Student 𝑡 copulas. The results show a clear general pattern: the test becomes more powerful when the sample size increases or when the change in dependence becomes larger. Small changes are harder to detect, especially for the feasible procedure based on local ranks. At the same time, the difference between the ideal and feasible procedures becomes smaller for larger samples and stronger changes in dependence. Overall, the thesis develops the theoretical justification for a likelihood-ratio change-point test in copula models and studies how the procedure behaves in finite samples.
...
Copulas are useful for studying how several random variables depend on each other, because they allow the dependence structure to be separated from the individual marginal distributions. This makes them particularly useful when the main interest is in whether the dependence itself changes over time. In this thesis, I study this problem for a multivariate time series whose dependence is described by a copula from a fixed parametric family. The main goal is to test whether the copula parameter remains constant over the whole sample or changes once at an unknown point in time. For each possible change-point, a model with one common copula parameter is compared with a model that allows different parameters before and after the split. Since the change location is unknown, the final test statistic is obtained by taking the largest value over a trimmed set of candidate change-points.
I first consider the ideal case, where the marginal distributions are known. In this setting, the true copula observations are available directly. The main difficulty is that the test does not use only one fixed split point, but searches over many possible locations. Therefore, the likelihood approximations need to hold uniformly over all candidate change-points. To do this, I first control the score process and the observed information matrices uniformly over the candidate splits. These results are then used to describe the estimation errors of the maximum likelihood estimators. From there, the likelihood ratio statistic can be rewritten as a quadratic form involving a centered score process. This process converges to a standard multivariate Brownian bridge, which gives the limiting distribution of the maximized test statistic.
The feasible case is more difficult because the marginal distributions are unknown. The true copula observations are then replaced by rank-based pseudo-observations. For every possible change-point, the ranks are recomputed separately in the two resulting segments. Because of this, the score terms are no longer simple partial sums of independent observations. To handle this, I use the sequential localrank empirical copula process and combine it with a function-indexed integration-by-parts argument. This makes it possible to derive the weak limit of the local-rank score process and, from this, the limiting distribution of the feasible likelihood ratio statistic. The resulting limit still has a Brownian-bridge-type structure, but its covariance also reflects the additional effect of estimating the marginal distributions through ranks.
Finally, I study the finite-sample behaviour of the test through simulations using Gaussian and Student 𝑡 copulas. The results show a clear general pattern: the test becomes more powerful when the sample size increases or when the change in dependence becomes larger. Small changes are harder to detect, especially for the feasible procedure based on local ranks. At the same time, the difference between the ideal and feasible procedures becomes smaller for larger samples and stronger changes in dependence. Overall, the thesis develops the theoretical justification for a likelihood-ratio change-point test in copula models and studies how the procedure behaves in finite samples.
I first consider the ideal case, where the marginal distributions are known. In this setting, the true copula observations are available directly. The main difficulty is that the test does not use only one fixed split point, but searches over many possible locations. Therefore, the likelihood approximations need to hold uniformly over all candidate change-points. To do this, I first control the score process and the observed information matrices uniformly over the candidate splits. These results are then used to describe the estimation errors of the maximum likelihood estimators. From there, the likelihood ratio statistic can be rewritten as a quadratic form involving a centered score process. This process converges to a standard multivariate Brownian bridge, which gives the limiting distribution of the maximized test statistic.
The feasible case is more difficult because the marginal distributions are unknown. The true copula observations are then replaced by rank-based pseudo-observations. For every possible change-point, the ranks are recomputed separately in the two resulting segments. Because of this, the score terms are no longer simple partial sums of independent observations. To handle this, I use the sequential localrank empirical copula process and combine it with a function-indexed integration-by-parts argument. This makes it possible to derive the weak limit of the local-rank score process and, from this, the limiting distribution of the feasible likelihood ratio statistic. The resulting limit still has a Brownian-bridge-type structure, but its covariance also reflects the additional effect of estimating the marginal distributions through ranks.
Finally, I study the finite-sample behaviour of the test through simulations using Gaussian and Student 𝑡 copulas. The results show a clear general pattern: the test becomes more powerful when the sample size increases or when the change in dependence becomes larger. Small changes are harder to detect, especially for the feasible procedure based on local ranks. At the same time, the difference between the ideal and feasible procedures becomes smaller for larger samples and stronger changes in dependence. Overall, the thesis develops the theoretical justification for a likelihood-ratio change-point test in copula models and studies how the procedure behaves in finite samples.
A Multi-State Markov Model for MS
Estimating Transition Probabilities from MSBase Data
Multiple Sclerosis (MS) is a chronic disease in which the immune system damages the protective myelin sheath surrounding nerve fibers in the central nervous system. Although there is no cure for MS, disease-modifying treatments (DMTs) can reduce disease activity and delay disease progression. The cost of these DMTs increased significantly over time, which highlights the need for cost-effective decision making regarding DMT use. The Erasmus MC/iMTA MS model is a microsimulation that represents individual patient trajectories to evaluate cost-effectiveness of MS treatments. Within this model, neurological disability is represented by a multistate Markov model using the msm package in R, where the states are defined according to the Expanded Disability Status Scale (EDSS) scores. Accurate transition probabilities are, therefore, required for this microsimulation.
This thesis develops a mathematical framework for estimating transition probabilities using a continuous-time Markov model and MSBase data. A simulation study was conducted to gain insight into the underlying estimation procedure and the incorporation of covariates. For the MSBase data analysis, inclusion criteria were constructed to align with the Erasmus MC/iMTA MS model. Several models were fitted with different specifications and choices of the covariates. Model selection was performed using the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and the log likelihood ratio test.
According to these criteria, the most complex model, including the most covariates and allowing some of them to vary across the transitions, provided the best fit among the models considered. The final model included gender, age, DMT group and continent, allowing age and DMT group to vary over all transitions. The resulting transition probabilities were analysed and visualized using plots of the predictions and Sankey diagrams. The covariate effects were interpreted using hazard ratios in the context of the model. The estimated transition probabilities were also compared with those reported in a previous MSBase study. This comparison revealed notable differences in the estimates, which may be attributed to the differences in population size, inclusion criteria and covariate specification.
...
This thesis develops a mathematical framework for estimating transition probabilities using a continuous-time Markov model and MSBase data. A simulation study was conducted to gain insight into the underlying estimation procedure and the incorporation of covariates. For the MSBase data analysis, inclusion criteria were constructed to align with the Erasmus MC/iMTA MS model. Several models were fitted with different specifications and choices of the covariates. Model selection was performed using the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and the log likelihood ratio test.
According to these criteria, the most complex model, including the most covariates and allowing some of them to vary across the transitions, provided the best fit among the models considered. The final model included gender, age, DMT group and continent, allowing age and DMT group to vary over all transitions. The resulting transition probabilities were analysed and visualized using plots of the predictions and Sankey diagrams. The covariate effects were interpreted using hazard ratios in the context of the model. The estimated transition probabilities were also compared with those reported in a previous MSBase study. This comparison revealed notable differences in the estimates, which may be attributed to the differences in population size, inclusion criteria and covariate specification.
...
Multiple Sclerosis (MS) is a chronic disease in which the immune system damages the protective myelin sheath surrounding nerve fibers in the central nervous system. Although there is no cure for MS, disease-modifying treatments (DMTs) can reduce disease activity and delay disease progression. The cost of these DMTs increased significantly over time, which highlights the need for cost-effective decision making regarding DMT use. The Erasmus MC/iMTA MS model is a microsimulation that represents individual patient trajectories to evaluate cost-effectiveness of MS treatments. Within this model, neurological disability is represented by a multistate Markov model using the msm package in R, where the states are defined according to the Expanded Disability Status Scale (EDSS) scores. Accurate transition probabilities are, therefore, required for this microsimulation.
This thesis develops a mathematical framework for estimating transition probabilities using a continuous-time Markov model and MSBase data. A simulation study was conducted to gain insight into the underlying estimation procedure and the incorporation of covariates. For the MSBase data analysis, inclusion criteria were constructed to align with the Erasmus MC/iMTA MS model. Several models were fitted with different specifications and choices of the covariates. Model selection was performed using the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and the log likelihood ratio test.
According to these criteria, the most complex model, including the most covariates and allowing some of them to vary across the transitions, provided the best fit among the models considered. The final model included gender, age, DMT group and continent, allowing age and DMT group to vary over all transitions. The resulting transition probabilities were analysed and visualized using plots of the predictions and Sankey diagrams. The covariate effects were interpreted using hazard ratios in the context of the model. The estimated transition probabilities were also compared with those reported in a previous MSBase study. This comparison revealed notable differences in the estimates, which may be attributed to the differences in population size, inclusion criteria and covariate specification.
This thesis develops a mathematical framework for estimating transition probabilities using a continuous-time Markov model and MSBase data. A simulation study was conducted to gain insight into the underlying estimation procedure and the incorporation of covariates. For the MSBase data analysis, inclusion criteria were constructed to align with the Erasmus MC/iMTA MS model. Several models were fitted with different specifications and choices of the covariates. Model selection was performed using the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and the log likelihood ratio test.
According to these criteria, the most complex model, including the most covariates and allowing some of them to vary across the transitions, provided the best fit among the models considered. The final model included gender, age, DMT group and continent, allowing age and DMT group to vary over all transitions. The resulting transition probabilities were analysed and visualized using plots of the predictions and Sankey diagrams. The covariate effects were interpreted using hazard ratios in the context of the model. The estimated transition probabilities were also compared with those reported in a previous MSBase study. This comparison revealed notable differences in the estimates, which may be attributed to the differences in population size, inclusion criteria and covariate specification.
In short Theory of Mind (ToM) is the ability to think about what someone else is thinking, with the added complexity of knowing that others might think differently than ourselves. On a more practical level this translates to choosing actions while keeping in mind what others are thinking about. These actions have to serve two purposes, the first one is to take advantage from this ability (exploitation), the second is to help us gather information to refine our knowledge about others (exploration). In the case where the dynamics unfold in a Partially Observable Markov Decision Process (POMDP), a framework that evaluates the cost of actions both from their exploratory, as well as their exploitative benefits, is the Active Inference Framework (AIF), whose formulas rely on an observation model P(o|s) and a preference distribution over states P(s).
At the moment, the area of the AIF dealing with cost of actions that keep others in mind is not fully developed and furthermore methods to learn the observation model and the preferences of others, so as to be able to model others over time, are still missing.
In this thesis we restricted ourselves to the case of a POMDP with finite number of states, observations and actions and only modeled the situation for two agents. We started by generalizing the overall formulation of the AIF by using beliefs about the observation model and the preferences of the other so as to encode the uncertainty we have about those quantities. We then extended the current theory of the AIF by proposing an action cost function which evaluates the cost of our actions while considering the presumed (re)actions of the other. Furthermore we developed methods to update the belief about the observation model and the preferences of the other, by using the actions the we see it take and the observations we see it receive. Finally we tested the central formulas of the AIF on a toy example to see if they work and also tested our function in a toy experiment, both in the case where the observation model of the other is given as well as in the case where it has to be learned. ...
At the moment, the area of the AIF dealing with cost of actions that keep others in mind is not fully developed and furthermore methods to learn the observation model and the preferences of others, so as to be able to model others over time, are still missing.
In this thesis we restricted ourselves to the case of a POMDP with finite number of states, observations and actions and only modeled the situation for two agents. We started by generalizing the overall formulation of the AIF by using beliefs about the observation model and the preferences of the other so as to encode the uncertainty we have about those quantities. We then extended the current theory of the AIF by proposing an action cost function which evaluates the cost of our actions while considering the presumed (re)actions of the other. Furthermore we developed methods to update the belief about the observation model and the preferences of the other, by using the actions the we see it take and the observations we see it receive. Finally we tested the central formulas of the AIF on a toy example to see if they work and also tested our function in a toy experiment, both in the case where the observation model of the other is given as well as in the case where it has to be learned. ...
In short Theory of Mind (ToM) is the ability to think about what someone else is thinking, with the added complexity of knowing that others might think differently than ourselves. On a more practical level this translates to choosing actions while keeping in mind what others are thinking about. These actions have to serve two purposes, the first one is to take advantage from this ability (exploitation), the second is to help us gather information to refine our knowledge about others (exploration). In the case where the dynamics unfold in a Partially Observable Markov Decision Process (POMDP), a framework that evaluates the cost of actions both from their exploratory, as well as their exploitative benefits, is the Active Inference Framework (AIF), whose formulas rely on an observation model P(o|s) and a preference distribution over states P(s).
At the moment, the area of the AIF dealing with cost of actions that keep others in mind is not fully developed and furthermore methods to learn the observation model and the preferences of others, so as to be able to model others over time, are still missing.
In this thesis we restricted ourselves to the case of a POMDP with finite number of states, observations and actions and only modeled the situation for two agents. We started by generalizing the overall formulation of the AIF by using beliefs about the observation model and the preferences of the other so as to encode the uncertainty we have about those quantities. We then extended the current theory of the AIF by proposing an action cost function which evaluates the cost of our actions while considering the presumed (re)actions of the other. Furthermore we developed methods to update the belief about the observation model and the preferences of the other, by using the actions the we see it take and the observations we see it receive. Finally we tested the central formulas of the AIF on a toy example to see if they work and also tested our function in a toy experiment, both in the case where the observation model of the other is given as well as in the case where it has to be learned.
At the moment, the area of the AIF dealing with cost of actions that keep others in mind is not fully developed and furthermore methods to learn the observation model and the preferences of others, so as to be able to model others over time, are still missing.
In this thesis we restricted ourselves to the case of a POMDP with finite number of states, observations and actions and only modeled the situation for two agents. We started by generalizing the overall formulation of the AIF by using beliefs about the observation model and the preferences of the other so as to encode the uncertainty we have about those quantities. We then extended the current theory of the AIF by proposing an action cost function which evaluates the cost of our actions while considering the presumed (re)actions of the other. Furthermore we developed methods to update the belief about the observation model and the preferences of the other, by using the actions the we see it take and the observations we see it receive. Finally we tested the central formulas of the AIF on a toy example to see if they work and also tested our function in a toy experiment, both in the case where the observation model of the other is given as well as in the case where it has to be learned.
Supporting the expert judgement process for quantifying uncertainties in policy research
A case study of the unique challenges with implementing structured expert elicitation for projecting policy effects
Master thesis
(2026)
-
T.K. Bolhuis, C. Wehrmann, Eva Kalmár, Shruti Setty, G.F. Nane, J. van Keulen
Expert opinions are crucial to quantify unknown variables when it is not feasible to use traditional research methods (limited resources or questions about future values). Implementing structured expert elicitation (SEE) is important for the quality and credibility of assumptions made by these experts or the researchers who enlist them. However, application in practice has been limited.
When research is performed to project policy effects, the context is so volatile that the accuracy of experts' judgements cannot be validated. Moreover, experts may focus on quantifying uncertainty while ignoring extreme uncertainties (war, future technological inventions), operating from a status quo point of view, in order to support the policy relevance of their research. This leads to a unique context of the expert judgement process. It is unclear how experts address expert judgement in this practice. Moreover, it is not yet known what problems may limit application of SEE protocols in this context.
I worked with the PBL Netherlands Environmental Assessment Agency to evaluate their expert judgement process for the KEV (The Climate and Energy Outlook). On a yearly basis their (sector) experts are required to judge dozens of uncertain variables for the projections of the progress on climate and energy goals. This includes policy effects, external factors like weather, and also scientific uncertainties like the inherent uncertainty of the models that are used for the projections.
How can practitioners in the policy research field be supported in implementing structured expert elicitation to improve their expert judgement?
To answer this research question and address it through communication design, I followed the Double Diamond method for design-based research (Discover-Define-Develop-Deliver). For the duration of a year, I was an intern at PBL, allowing me to observe and discuss their methodology, while inquiring after what problems they face. I helped organise a pilot for implementation of the IDEA protocol for structured expert elicitation. To evaluate this pilot I designed a focus group session with all different actors involved in the KEV project. Next, to discuss challenges and develop possible solutions I organised a co-design workshop with (sector) experts from different teams that work on the KEV.
The results show that experts face several unique challenges in their expert judgement process, which are not directly addressed by SEE protocols. The IDEA protocol shows promise to improve quality of judgements and transparency through increased documentation. However, the protocol lacks support experts say they require to select what uncertainties to address in their research, as well as adequate support to quantify their uncertainty interval.
Siloed teams lead to diverging methodology and definitions, as well as missing overall problem demarcation. Because there is limited opportunity for feedback on the accuracy of experts' judgements, there is no universal measure of what makes a judgement 'good'.
To address the problems faced by the practitioners at PBL, I designed an instructional video. It informs experts about SEE and provides tangible examples and actionable steps the practitioners can take on the short and long term, on the individual and organisational level. This provides the researchers with the knowledge and control to improve their own practice. At the same time, the video also acknowledges the unique challenges the experts face and reassures them of the confidence they can have in their practice to make decisions. By targeting both teamleaders and sector experts, the facilitating party and the practicing party are involved and given agency in this process.
Therefore, research requiring expert judgement on policy uncertainties presents some unique challenges in the expert judgement process. When accuracy cannot be used as a measure of quality, it is important that the researchers invest in the credibility of the methodology. SEE can provide structure and transparency, but additional instructions and methods are needed to support experts to confidently make judgements that balance accuracy and information.
Though this case study focuses on a specific organisation and group of experts, the lessons learned from this study indicate a variety of challenges when applying SEE in different research domains and contexts. This could possible indicate the stagnated implementation in practice. Additionally, this research and the development of structured expert elicitation for policy assessment support credibility of expert judgement in this political environment. ...
When research is performed to project policy effects, the context is so volatile that the accuracy of experts' judgements cannot be validated. Moreover, experts may focus on quantifying uncertainty while ignoring extreme uncertainties (war, future technological inventions), operating from a status quo point of view, in order to support the policy relevance of their research. This leads to a unique context of the expert judgement process. It is unclear how experts address expert judgement in this practice. Moreover, it is not yet known what problems may limit application of SEE protocols in this context.
I worked with the PBL Netherlands Environmental Assessment Agency to evaluate their expert judgement process for the KEV (The Climate and Energy Outlook). On a yearly basis their (sector) experts are required to judge dozens of uncertain variables for the projections of the progress on climate and energy goals. This includes policy effects, external factors like weather, and also scientific uncertainties like the inherent uncertainty of the models that are used for the projections.
How can practitioners in the policy research field be supported in implementing structured expert elicitation to improve their expert judgement?
To answer this research question and address it through communication design, I followed the Double Diamond method for design-based research (Discover-Define-Develop-Deliver). For the duration of a year, I was an intern at PBL, allowing me to observe and discuss their methodology, while inquiring after what problems they face. I helped organise a pilot for implementation of the IDEA protocol for structured expert elicitation. To evaluate this pilot I designed a focus group session with all different actors involved in the KEV project. Next, to discuss challenges and develop possible solutions I organised a co-design workshop with (sector) experts from different teams that work on the KEV.
The results show that experts face several unique challenges in their expert judgement process, which are not directly addressed by SEE protocols. The IDEA protocol shows promise to improve quality of judgements and transparency through increased documentation. However, the protocol lacks support experts say they require to select what uncertainties to address in their research, as well as adequate support to quantify their uncertainty interval.
Siloed teams lead to diverging methodology and definitions, as well as missing overall problem demarcation. Because there is limited opportunity for feedback on the accuracy of experts' judgements, there is no universal measure of what makes a judgement 'good'.
To address the problems faced by the practitioners at PBL, I designed an instructional video. It informs experts about SEE and provides tangible examples and actionable steps the practitioners can take on the short and long term, on the individual and organisational level. This provides the researchers with the knowledge and control to improve their own practice. At the same time, the video also acknowledges the unique challenges the experts face and reassures them of the confidence they can have in their practice to make decisions. By targeting both teamleaders and sector experts, the facilitating party and the practicing party are involved and given agency in this process.
Therefore, research requiring expert judgement on policy uncertainties presents some unique challenges in the expert judgement process. When accuracy cannot be used as a measure of quality, it is important that the researchers invest in the credibility of the methodology. SEE can provide structure and transparency, but additional instructions and methods are needed to support experts to confidently make judgements that balance accuracy and information.
Though this case study focuses on a specific organisation and group of experts, the lessons learned from this study indicate a variety of challenges when applying SEE in different research domains and contexts. This could possible indicate the stagnated implementation in practice. Additionally, this research and the development of structured expert elicitation for policy assessment support credibility of expert judgement in this political environment. ...
Expert opinions are crucial to quantify unknown variables when it is not feasible to use traditional research methods (limited resources or questions about future values). Implementing structured expert elicitation (SEE) is important for the quality and credibility of assumptions made by these experts or the researchers who enlist them. However, application in practice has been limited.
When research is performed to project policy effects, the context is so volatile that the accuracy of experts' judgements cannot be validated. Moreover, experts may focus on quantifying uncertainty while ignoring extreme uncertainties (war, future technological inventions), operating from a status quo point of view, in order to support the policy relevance of their research. This leads to a unique context of the expert judgement process. It is unclear how experts address expert judgement in this practice. Moreover, it is not yet known what problems may limit application of SEE protocols in this context.
I worked with the PBL Netherlands Environmental Assessment Agency to evaluate their expert judgement process for the KEV (The Climate and Energy Outlook). On a yearly basis their (sector) experts are required to judge dozens of uncertain variables for the projections of the progress on climate and energy goals. This includes policy effects, external factors like weather, and also scientific uncertainties like the inherent uncertainty of the models that are used for the projections.
How can practitioners in the policy research field be supported in implementing structured expert elicitation to improve their expert judgement?
To answer this research question and address it through communication design, I followed the Double Diamond method for design-based research (Discover-Define-Develop-Deliver). For the duration of a year, I was an intern at PBL, allowing me to observe and discuss their methodology, while inquiring after what problems they face. I helped organise a pilot for implementation of the IDEA protocol for structured expert elicitation. To evaluate this pilot I designed a focus group session with all different actors involved in the KEV project. Next, to discuss challenges and develop possible solutions I organised a co-design workshop with (sector) experts from different teams that work on the KEV.
The results show that experts face several unique challenges in their expert judgement process, which are not directly addressed by SEE protocols. The IDEA protocol shows promise to improve quality of judgements and transparency through increased documentation. However, the protocol lacks support experts say they require to select what uncertainties to address in their research, as well as adequate support to quantify their uncertainty interval.
Siloed teams lead to diverging methodology and definitions, as well as missing overall problem demarcation. Because there is limited opportunity for feedback on the accuracy of experts' judgements, there is no universal measure of what makes a judgement 'good'.
To address the problems faced by the practitioners at PBL, I designed an instructional video. It informs experts about SEE and provides tangible examples and actionable steps the practitioners can take on the short and long term, on the individual and organisational level. This provides the researchers with the knowledge and control to improve their own practice. At the same time, the video also acknowledges the unique challenges the experts face and reassures them of the confidence they can have in their practice to make decisions. By targeting both teamleaders and sector experts, the facilitating party and the practicing party are involved and given agency in this process.
Therefore, research requiring expert judgement on policy uncertainties presents some unique challenges in the expert judgement process. When accuracy cannot be used as a measure of quality, it is important that the researchers invest in the credibility of the methodology. SEE can provide structure and transparency, but additional instructions and methods are needed to support experts to confidently make judgements that balance accuracy and information.
Though this case study focuses on a specific organisation and group of experts, the lessons learned from this study indicate a variety of challenges when applying SEE in different research domains and contexts. This could possible indicate the stagnated implementation in practice. Additionally, this research and the development of structured expert elicitation for policy assessment support credibility of expert judgement in this political environment.
When research is performed to project policy effects, the context is so volatile that the accuracy of experts' judgements cannot be validated. Moreover, experts may focus on quantifying uncertainty while ignoring extreme uncertainties (war, future technological inventions), operating from a status quo point of view, in order to support the policy relevance of their research. This leads to a unique context of the expert judgement process. It is unclear how experts address expert judgement in this practice. Moreover, it is not yet known what problems may limit application of SEE protocols in this context.
I worked with the PBL Netherlands Environmental Assessment Agency to evaluate their expert judgement process for the KEV (The Climate and Energy Outlook). On a yearly basis their (sector) experts are required to judge dozens of uncertain variables for the projections of the progress on climate and energy goals. This includes policy effects, external factors like weather, and also scientific uncertainties like the inherent uncertainty of the models that are used for the projections.
How can practitioners in the policy research field be supported in implementing structured expert elicitation to improve their expert judgement?
To answer this research question and address it through communication design, I followed the Double Diamond method for design-based research (Discover-Define-Develop-Deliver). For the duration of a year, I was an intern at PBL, allowing me to observe and discuss their methodology, while inquiring after what problems they face. I helped organise a pilot for implementation of the IDEA protocol for structured expert elicitation. To evaluate this pilot I designed a focus group session with all different actors involved in the KEV project. Next, to discuss challenges and develop possible solutions I organised a co-design workshop with (sector) experts from different teams that work on the KEV.
The results show that experts face several unique challenges in their expert judgement process, which are not directly addressed by SEE protocols. The IDEA protocol shows promise to improve quality of judgements and transparency through increased documentation. However, the protocol lacks support experts say they require to select what uncertainties to address in their research, as well as adequate support to quantify their uncertainty interval.
Siloed teams lead to diverging methodology and definitions, as well as missing overall problem demarcation. Because there is limited opportunity for feedback on the accuracy of experts' judgements, there is no universal measure of what makes a judgement 'good'.
To address the problems faced by the practitioners at PBL, I designed an instructional video. It informs experts about SEE and provides tangible examples and actionable steps the practitioners can take on the short and long term, on the individual and organisational level. This provides the researchers with the knowledge and control to improve their own practice. At the same time, the video also acknowledges the unique challenges the experts face and reassures them of the confidence they can have in their practice to make decisions. By targeting both teamleaders and sector experts, the facilitating party and the practicing party are involved and given agency in this process.
Therefore, research requiring expert judgement on policy uncertainties presents some unique challenges in the expert judgement process. When accuracy cannot be used as a measure of quality, it is important that the researchers invest in the credibility of the methodology. SEE can provide structure and transparency, but additional instructions and methods are needed to support experts to confidently make judgements that balance accuracy and information.
Though this case study focuses on a specific organisation and group of experts, the lessons learned from this study indicate a variety of challenges when applying SEE in different research domains and contexts. This could possible indicate the stagnated implementation in practice. Additionally, this research and the development of structured expert elicitation for policy assessment support credibility of expert judgement in this political environment.
The increasing integration of Renewable Energy Sources (RES), rising global electricity demand, and ongoing developments in power market structures collectively increase the complexity of Energy Management Systems (EMS). The tight scheduling of interdependent decisions in a Rolling Horizon (RH) Mixed Integer Linear Programming (MILP) environment requires efficient formulations to remain scalable and flexible to future innovations. This thesis investigates initialization strategies (warm starts) that leverage previous optimal system configurations to reduce computational complexity and solution time. Iterative cycles of variable selection, warm start execution, and problem reformulation are evaluated across multiple scenarios. These scenarios vary in modeling horizon, day-ahead price profiles, market engagement strategies, and environmental and system conditions. Problem reformulations include adjustments in the treatment of violation decision variables, linear reformulations, and the use of Benders decomposition. The results demonstrate that successful warm start implementations can substantially reduce solution times and provide valuable insights for further tightening problem formulations. Overall, the study provides guidance on efficient formulations that support effective initialization and enhance solver performance across a wide range of users and system configurations, thereby contributing to more scalable and widely applicable energy optimization practices. Keywords: Rolling Horizon (RH), Warm Start, Unit Commitment (UC), Mixed Integer Linear Programming (MILP), Benders Decomposition
...
The increasing integration of Renewable Energy Sources (RES), rising global electricity demand, and ongoing developments in power market structures collectively increase the complexity of Energy Management Systems (EMS). The tight scheduling of interdependent decisions in a Rolling Horizon (RH) Mixed Integer Linear Programming (MILP) environment requires efficient formulations to remain scalable and flexible to future innovations. This thesis investigates initialization strategies (warm starts) that leverage previous optimal system configurations to reduce computational complexity and solution time. Iterative cycles of variable selection, warm start execution, and problem reformulation are evaluated across multiple scenarios. These scenarios vary in modeling horizon, day-ahead price profiles, market engagement strategies, and environmental and system conditions. Problem reformulations include adjustments in the treatment of violation decision variables, linear reformulations, and the use of Benders decomposition. The results demonstrate that successful warm start implementations can substantially reduce solution times and provide valuable insights for further tightening problem formulations. Overall, the study provides guidance on efficient formulations that support effective initialization and enhance solver performance across a wide range of users and system configurations, thereby contributing to more scalable and widely applicable energy optimization practices. Keywords: Rolling Horizon (RH), Warm Start, Unit Commitment (UC), Mixed Integer Linear Programming (MILP), Benders Decomposition
The Mathematical Validation of AI
A Case Study on Bias Reduction in the Fraud Risk Model of the Municipality of Rotterdam
This study critically examines the fairness of Rotterdam’s fraud detection system using the Lighthouse Reports’ Suspicion Machine framework. By replicating and extending the original model with gradient boosting, dimension- ality reduction (PCA), clustering, and adversarial debiasing, the analysis highlights how small changes in input or weighting can substantially alter bias across predefined archetypes. Although clustering revealed no clear separa- tion in risk scores, weighting and adversarial techniques reduced disparities between groups. Limitations include the synthetic nature of the dataset, lack of real fraud labels, and restricted focus on 13 archetypes. The findings stress the importance of validating input data and model design, as fairness outcomes remain highly sensitive to methodological choices.
...
This study critically examines the fairness of Rotterdam’s fraud detection system using the Lighthouse Reports’ Suspicion Machine framework. By replicating and extending the original model with gradient boosting, dimension- ality reduction (PCA), clustering, and adversarial debiasing, the analysis highlights how small changes in input or weighting can substantially alter bias across predefined archetypes. Although clustering revealed no clear separa- tion in risk scores, weighting and adversarial techniques reduced disparities between groups. Limitations include the synthetic nature of the dataset, lack of real fraud labels, and restricted focus on 13 archetypes. The findings stress the importance of validating input data and model design, as fairness outcomes remain highly sensitive to methodological choices.
Semiparametric dependence modeling in illiquid financial markets using multivariate zero‐inflated GARCH‐X models
Case study on Voluntary Carbon Credits in collaboration with Rabobank
Master thesis
(2025)
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J.L. Vlak, A.F.F. Derumigny, G.F. Nane, Leon Boerop, Modesta Van Aken, Emma Van de Ven
Voluntary carbon markets are at an early stage of development, characterized by low and irregular trading frequency. Such limited activity results in extended periods of unchanged prices and a high incidence of zero returns, making voluntary carbon markets a typical example of illiquid financial markets. To model dependence in such settings, we propose a multivariate zero-inflated GARCH-X model. The model extends the existing zero-inflated GARCH model to a multivariate setup, incorporating both a GARCH-X component with binary trading indicators as exogenous covariates and a time-step specification that updates only when trades occur.
The multivariate extension incorporates two different types of dependence. First, cross-dependence in trading activity is modeled using Markov networks applied to binary trading indicators. Second, cross-dependence in returns is analyzed using a copula-GARCH framework applied to residuals, with residuals corresponding to zero returns treated as undefined values. To make copula methods applicable to zero-inflated data, we introduce a joint probability integral transform approach. In this construction, the univariate marginals are defined conditional on the simultaneous trading activity of each asset, rather than conditioning only on each asset’s own trading activity. We prove that this method yields a consistent copula estimator when applied to the subset of observations where all assets have simultaneous non-zero trading activity. Dependence is quantified using both unconditional and conditional Kendall’s tau, estimated via kernel-based methods.
Theoretical results include consistency and asymptotic normality of the quasi-maximum likelihood estimator for the multivariate model under stationary covariates. The empirical study covers seven voluntary carbon credits and six conventional financial assets. We find no significant dependence between carbon credits and conventional assets, but observe strong correlation within the carbon market, especially among nature-based credits. Results suggest that voluntary carbon markets may operate independently of more liquid assets and are influenced by peer pricing due to a lack of standardization. ...
The multivariate extension incorporates two different types of dependence. First, cross-dependence in trading activity is modeled using Markov networks applied to binary trading indicators. Second, cross-dependence in returns is analyzed using a copula-GARCH framework applied to residuals, with residuals corresponding to zero returns treated as undefined values. To make copula methods applicable to zero-inflated data, we introduce a joint probability integral transform approach. In this construction, the univariate marginals are defined conditional on the simultaneous trading activity of each asset, rather than conditioning only on each asset’s own trading activity. We prove that this method yields a consistent copula estimator when applied to the subset of observations where all assets have simultaneous non-zero trading activity. Dependence is quantified using both unconditional and conditional Kendall’s tau, estimated via kernel-based methods.
Theoretical results include consistency and asymptotic normality of the quasi-maximum likelihood estimator for the multivariate model under stationary covariates. The empirical study covers seven voluntary carbon credits and six conventional financial assets. We find no significant dependence between carbon credits and conventional assets, but observe strong correlation within the carbon market, especially among nature-based credits. Results suggest that voluntary carbon markets may operate independently of more liquid assets and are influenced by peer pricing due to a lack of standardization. ...
Voluntary carbon markets are at an early stage of development, characterized by low and irregular trading frequency. Such limited activity results in extended periods of unchanged prices and a high incidence of zero returns, making voluntary carbon markets a typical example of illiquid financial markets. To model dependence in such settings, we propose a multivariate zero-inflated GARCH-X model. The model extends the existing zero-inflated GARCH model to a multivariate setup, incorporating both a GARCH-X component with binary trading indicators as exogenous covariates and a time-step specification that updates only when trades occur.
The multivariate extension incorporates two different types of dependence. First, cross-dependence in trading activity is modeled using Markov networks applied to binary trading indicators. Second, cross-dependence in returns is analyzed using a copula-GARCH framework applied to residuals, with residuals corresponding to zero returns treated as undefined values. To make copula methods applicable to zero-inflated data, we introduce a joint probability integral transform approach. In this construction, the univariate marginals are defined conditional on the simultaneous trading activity of each asset, rather than conditioning only on each asset’s own trading activity. We prove that this method yields a consistent copula estimator when applied to the subset of observations where all assets have simultaneous non-zero trading activity. Dependence is quantified using both unconditional and conditional Kendall’s tau, estimated via kernel-based methods.
Theoretical results include consistency and asymptotic normality of the quasi-maximum likelihood estimator for the multivariate model under stationary covariates. The empirical study covers seven voluntary carbon credits and six conventional financial assets. We find no significant dependence between carbon credits and conventional assets, but observe strong correlation within the carbon market, especially among nature-based credits. Results suggest that voluntary carbon markets may operate independently of more liquid assets and are influenced by peer pricing due to a lack of standardization.
The multivariate extension incorporates two different types of dependence. First, cross-dependence in trading activity is modeled using Markov networks applied to binary trading indicators. Second, cross-dependence in returns is analyzed using a copula-GARCH framework applied to residuals, with residuals corresponding to zero returns treated as undefined values. To make copula methods applicable to zero-inflated data, we introduce a joint probability integral transform approach. In this construction, the univariate marginals are defined conditional on the simultaneous trading activity of each asset, rather than conditioning only on each asset’s own trading activity. We prove that this method yields a consistent copula estimator when applied to the subset of observations where all assets have simultaneous non-zero trading activity. Dependence is quantified using both unconditional and conditional Kendall’s tau, estimated via kernel-based methods.
Theoretical results include consistency and asymptotic normality of the quasi-maximum likelihood estimator for the multivariate model under stationary covariates. The empirical study covers seven voluntary carbon credits and six conventional financial assets. We find no significant dependence between carbon credits and conventional assets, but observe strong correlation within the carbon market, especially among nature-based credits. Results suggest that voluntary carbon markets may operate independently of more liquid assets and are influenced by peer pricing due to a lack of standardization.
This thesis investigates optimization-based control allocation methods designed for fault-tolerant and scalable application in multi-stage rockets. It is particularly focused on rockets with Thrust Vector Control (TVC), aerodynamic fins and Reaction Control Systems (RCS). The aim is to minimize the error between control commands and actuator output, besides actuator effort. Both in nominal and faulty conditions. Three convex optimization formulations are proposed: an Angle-Deflection (AD) problem, a linearized problem and a Second-Order Cone Programming (SOCP) problem. The AD problem includes actuator deflections and the linearized and SOCP formulations jointly consider actuator deflections and engine throttling. This work allows integration of faulty scenarios by constraint tightening, allowing reconfiguration of control allocation without changing the problem structure. Simulation data is used to validate the effectiveness of the formulations in satisfying control commands and fault handling. The work contributes to fault-tolerant and scalable control allocation frameworks.
...
This thesis investigates optimization-based control allocation methods designed for fault-tolerant and scalable application in multi-stage rockets. It is particularly focused on rockets with Thrust Vector Control (TVC), aerodynamic fins and Reaction Control Systems (RCS). The aim is to minimize the error between control commands and actuator output, besides actuator effort. Both in nominal and faulty conditions. Three convex optimization formulations are proposed: an Angle-Deflection (AD) problem, a linearized problem and a Second-Order Cone Programming (SOCP) problem. The AD problem includes actuator deflections and the linearized and SOCP formulations jointly consider actuator deflections and engine throttling. This work allows integration of faulty scenarios by constraint tightening, allowing reconfiguration of control allocation without changing the problem structure. Simulation data is used to validate the effectiveness of the formulations in satisfying control commands and fault handling. The work contributes to fault-tolerant and scalable control allocation frameworks.
Combinability in meta-analysis of multi-treatment observational studies
Assessing and minimising covariate imbalance
Meta-analysis is a powerful method to combine the treatment effects of multiple independent studies answering a common research question. To determine a causal treatment effect in a meta-analysis it is important to look at the characteristics of the participants, like age or diseases, also known as covariates. In the case of experimental studies, participants are randomly allocated to treatment groups. As a result, the covariate is in expectation equally distributed between the treatment groups. In observational studies, no randomisation has occurred and thus, the covariate imbalance between treatment groups may be more profound. This makes it difficult to determine a causal effect of the treatment, since the covariate may affect the outcome. Therefore, it is important to balance these covariates between the treatment, especially for observational studies. The condition when this balance is present is called combinability.
In this thesis, the covariate imbalance between treatment groups is assessed using five multi-sample test statistics. These assessment methods are based on the comparison of the empirical cumulative distribution functions of the covariate between the meta-arms, which are the collections of the similar treatment groups. Then, a permutation test is used to determine whether the covariate imbalance is significant, as assessed by the multi-sample test statistics. This is done by computing a distribution of the multi-sample test statistics under the null hypothesis that there is no covariate imbalance between the meta-arms. If the observed multi-sample test statistics are significantly large, then combinability is not satisfied.
Subsequently, a balancing procedure is proposed to minimise the covariate imbalance if combinability is not satisfied. This balancing procedure works by discarding a selection of treatment groups from the meta-analysis, such that the multi-sample test statistics indicate that the covariate imbalance is no longer significant. The result is a more combinable set of treatment groups that can be used for the purposes of meta-analysis. Finally, a simulation study of the balancing procedure is done for three and four treatment groups. In these simulations, the treatment groups are simulated with different underlying distributions, such that in theory the covariate imbalance is significant. These simulations seem to indicate that the more treatment groups there are, the more groups need to be discarded before the covariate imbalance is no longer significant. This is explained by the fact that the initial covariate imbalance is larger if there are more treatment groups. On average, in the case of three treatment groups, nearly a fifth of groups needs to discarded, while in in the case of four treatment groups, roughly a third of groups needs to be discarded. Finally the use of five multi-sample test statistics in the balancing procedure result in a sizeable overlap of groups that are discarded. ...
In this thesis, the covariate imbalance between treatment groups is assessed using five multi-sample test statistics. These assessment methods are based on the comparison of the empirical cumulative distribution functions of the covariate between the meta-arms, which are the collections of the similar treatment groups. Then, a permutation test is used to determine whether the covariate imbalance is significant, as assessed by the multi-sample test statistics. This is done by computing a distribution of the multi-sample test statistics under the null hypothesis that there is no covariate imbalance between the meta-arms. If the observed multi-sample test statistics are significantly large, then combinability is not satisfied.
Subsequently, a balancing procedure is proposed to minimise the covariate imbalance if combinability is not satisfied. This balancing procedure works by discarding a selection of treatment groups from the meta-analysis, such that the multi-sample test statistics indicate that the covariate imbalance is no longer significant. The result is a more combinable set of treatment groups that can be used for the purposes of meta-analysis. Finally, a simulation study of the balancing procedure is done for three and four treatment groups. In these simulations, the treatment groups are simulated with different underlying distributions, such that in theory the covariate imbalance is significant. These simulations seem to indicate that the more treatment groups there are, the more groups need to be discarded before the covariate imbalance is no longer significant. This is explained by the fact that the initial covariate imbalance is larger if there are more treatment groups. On average, in the case of three treatment groups, nearly a fifth of groups needs to discarded, while in in the case of four treatment groups, roughly a third of groups needs to be discarded. Finally the use of five multi-sample test statistics in the balancing procedure result in a sizeable overlap of groups that are discarded. ...
Meta-analysis is a powerful method to combine the treatment effects of multiple independent studies answering a common research question. To determine a causal treatment effect in a meta-analysis it is important to look at the characteristics of the participants, like age or diseases, also known as covariates. In the case of experimental studies, participants are randomly allocated to treatment groups. As a result, the covariate is in expectation equally distributed between the treatment groups. In observational studies, no randomisation has occurred and thus, the covariate imbalance between treatment groups may be more profound. This makes it difficult to determine a causal effect of the treatment, since the covariate may affect the outcome. Therefore, it is important to balance these covariates between the treatment, especially for observational studies. The condition when this balance is present is called combinability.
In this thesis, the covariate imbalance between treatment groups is assessed using five multi-sample test statistics. These assessment methods are based on the comparison of the empirical cumulative distribution functions of the covariate between the meta-arms, which are the collections of the similar treatment groups. Then, a permutation test is used to determine whether the covariate imbalance is significant, as assessed by the multi-sample test statistics. This is done by computing a distribution of the multi-sample test statistics under the null hypothesis that there is no covariate imbalance between the meta-arms. If the observed multi-sample test statistics are significantly large, then combinability is not satisfied.
Subsequently, a balancing procedure is proposed to minimise the covariate imbalance if combinability is not satisfied. This balancing procedure works by discarding a selection of treatment groups from the meta-analysis, such that the multi-sample test statistics indicate that the covariate imbalance is no longer significant. The result is a more combinable set of treatment groups that can be used for the purposes of meta-analysis. Finally, a simulation study of the balancing procedure is done for three and four treatment groups. In these simulations, the treatment groups are simulated with different underlying distributions, such that in theory the covariate imbalance is significant. These simulations seem to indicate that the more treatment groups there are, the more groups need to be discarded before the covariate imbalance is no longer significant. This is explained by the fact that the initial covariate imbalance is larger if there are more treatment groups. On average, in the case of three treatment groups, nearly a fifth of groups needs to discarded, while in in the case of four treatment groups, roughly a third of groups needs to be discarded. Finally the use of five multi-sample test statistics in the balancing procedure result in a sizeable overlap of groups that are discarded.
In this thesis, the covariate imbalance between treatment groups is assessed using five multi-sample test statistics. These assessment methods are based on the comparison of the empirical cumulative distribution functions of the covariate between the meta-arms, which are the collections of the similar treatment groups. Then, a permutation test is used to determine whether the covariate imbalance is significant, as assessed by the multi-sample test statistics. This is done by computing a distribution of the multi-sample test statistics under the null hypothesis that there is no covariate imbalance between the meta-arms. If the observed multi-sample test statistics are significantly large, then combinability is not satisfied.
Subsequently, a balancing procedure is proposed to minimise the covariate imbalance if combinability is not satisfied. This balancing procedure works by discarding a selection of treatment groups from the meta-analysis, such that the multi-sample test statistics indicate that the covariate imbalance is no longer significant. The result is a more combinable set of treatment groups that can be used for the purposes of meta-analysis. Finally, a simulation study of the balancing procedure is done for three and four treatment groups. In these simulations, the treatment groups are simulated with different underlying distributions, such that in theory the covariate imbalance is significant. These simulations seem to indicate that the more treatment groups there are, the more groups need to be discarded before the covariate imbalance is no longer significant. This is explained by the fact that the initial covariate imbalance is larger if there are more treatment groups. On average, in the case of three treatment groups, nearly a fifth of groups needs to discarded, while in in the case of four treatment groups, roughly a third of groups needs to be discarded. Finally the use of five multi-sample test statistics in the balancing procedure result in a sizeable overlap of groups that are discarded.
We consider the problem of online nonparametric regression for signals of length n with total variation at most Cn whose observations are contaminated by σ-subgaussian noise. While there exist many algorithms which achieve optimal performance under the assumption of independent noise, this work focusses on the less explored general case of dependent noise. We focus on the Follow-the-Leading-History (FLH) algorithm, a powerful meta-aggregation method for online learning.
We prove that under mild assumptions of weak long-range dependence, we may apply FLH to m ≈ log n partitioned data streams to mitigate high correlations. We show that the resulting algorithm Thinned-FLH (TFLH) achieves the minimax optimal cumulative error rate of O(n^(1/3)C_n^(2/3)) with high probability, matching the performance in the independent case up to logarithmic factors. We also conduct a simulation study, which validates our theoretical findings and demonstrates that TFLH may outperform FLH in high dependence environments in spite of the data thinning. ...
We prove that under mild assumptions of weak long-range dependence, we may apply FLH to m ≈ log n partitioned data streams to mitigate high correlations. We show that the resulting algorithm Thinned-FLH (TFLH) achieves the minimax optimal cumulative error rate of O(n^(1/3)C_n^(2/3)) with high probability, matching the performance in the independent case up to logarithmic factors. We also conduct a simulation study, which validates our theoretical findings and demonstrates that TFLH may outperform FLH in high dependence environments in spite of the data thinning. ...
We consider the problem of online nonparametric regression for signals of length n with total variation at most Cn whose observations are contaminated by σ-subgaussian noise. While there exist many algorithms which achieve optimal performance under the assumption of independent noise, this work focusses on the less explored general case of dependent noise. We focus on the Follow-the-Leading-History (FLH) algorithm, a powerful meta-aggregation method for online learning.
We prove that under mild assumptions of weak long-range dependence, we may apply FLH to m ≈ log n partitioned data streams to mitigate high correlations. We show that the resulting algorithm Thinned-FLH (TFLH) achieves the minimax optimal cumulative error rate of O(n^(1/3)C_n^(2/3)) with high probability, matching the performance in the independent case up to logarithmic factors. We also conduct a simulation study, which validates our theoretical findings and demonstrates that TFLH may outperform FLH in high dependence environments in spite of the data thinning.
We prove that under mild assumptions of weak long-range dependence, we may apply FLH to m ≈ log n partitioned data streams to mitigate high correlations. We show that the resulting algorithm Thinned-FLH (TFLH) achieves the minimax optimal cumulative error rate of O(n^(1/3)C_n^(2/3)) with high probability, matching the performance in the independent case up to logarithmic factors. We also conduct a simulation study, which validates our theoretical findings and demonstrates that TFLH may outperform FLH in high dependence environments in spite of the data thinning.
Accurate early prognostication after pediatric cardiac arrest is clinically crucial yet remains methodologically challenging. This thesis frames the problem as a representation learning task on raw electroencephalography (EEG) and introduces a fully self-supervised pipeline followed by a supervised classifier. A Time-Series-to-Vector (TS2Vec) encoder is trained on 6,669 unlabeled twenty-second EEG epochs (T = 2000 time points, C = 4 channels) from 84 comatose children treated at Erasmus MC Sophia Children’s Hospital. The encoder learns to map each EEG epoch to a 320-dimensional vector by contrasting transformed views of the same signal from unrelated signals, without using outcome labels.
Downstream classification is performed with a k-nearest neighbors (k-NN) model. Probabilities are assigned at the epoch level and aggregated across all epochs of a patient to generate a final patientlevel prognosis. Five-fold patient-level cross-validation gives an area under the ROC curve of 0.861 ± 0.092, an accuracy of 0.774±0.045 and an F1 score of 0.733±0.057. Critically, specificity and precision are both 1.000 ± 0.000. Thus the model never predicts death for a child who survives, satisfying a stringent clinical safety requirement. Sensitivity is 0.581 ± 0.070, reflecting a deliberately conservative decision threshold.
Qualitative analyses offers tentative support for the physiological relevance of the learned features. t-SNE projections show clustering by patient identity and good separation between the two extreme EEG background patterns (continuous normal activity and electrocerebral silence) without supervision. Saliency analysis did not yield clinically interpretable patterns.
Compared to the leading feature-engineered qEEG baseline, the proposed approach achieves equivalent specificity and a slightly lower AUC, while removing the need for manual feature design and expert annotation. The modular architecture invites several extensions, including graph-based encoders that respect electrode topology, integration of auxiliary data such as ECG and clinical metadata, retrieval-based reasoning using large historical EEG archives, and more interpretable or end-to-end trainable models. Overall, this work demonstrates that contrastive learning can be effectively applied to raw pediatric EEG for conservative, label-efficient outcome prediction after cardiac arrest, and offers a mathematically grounded proof of concept for future clinical applications. ...
Downstream classification is performed with a k-nearest neighbors (k-NN) model. Probabilities are assigned at the epoch level and aggregated across all epochs of a patient to generate a final patientlevel prognosis. Five-fold patient-level cross-validation gives an area under the ROC curve of 0.861 ± 0.092, an accuracy of 0.774±0.045 and an F1 score of 0.733±0.057. Critically, specificity and precision are both 1.000 ± 0.000. Thus the model never predicts death for a child who survives, satisfying a stringent clinical safety requirement. Sensitivity is 0.581 ± 0.070, reflecting a deliberately conservative decision threshold.
Qualitative analyses offers tentative support for the physiological relevance of the learned features. t-SNE projections show clustering by patient identity and good separation between the two extreme EEG background patterns (continuous normal activity and electrocerebral silence) without supervision. Saliency analysis did not yield clinically interpretable patterns.
Compared to the leading feature-engineered qEEG baseline, the proposed approach achieves equivalent specificity and a slightly lower AUC, while removing the need for manual feature design and expert annotation. The modular architecture invites several extensions, including graph-based encoders that respect electrode topology, integration of auxiliary data such as ECG and clinical metadata, retrieval-based reasoning using large historical EEG archives, and more interpretable or end-to-end trainable models. Overall, this work demonstrates that contrastive learning can be effectively applied to raw pediatric EEG for conservative, label-efficient outcome prediction after cardiac arrest, and offers a mathematically grounded proof of concept for future clinical applications. ...
Accurate early prognostication after pediatric cardiac arrest is clinically crucial yet remains methodologically challenging. This thesis frames the problem as a representation learning task on raw electroencephalography (EEG) and introduces a fully self-supervised pipeline followed by a supervised classifier. A Time-Series-to-Vector (TS2Vec) encoder is trained on 6,669 unlabeled twenty-second EEG epochs (T = 2000 time points, C = 4 channels) from 84 comatose children treated at Erasmus MC Sophia Children’s Hospital. The encoder learns to map each EEG epoch to a 320-dimensional vector by contrasting transformed views of the same signal from unrelated signals, without using outcome labels.
Downstream classification is performed with a k-nearest neighbors (k-NN) model. Probabilities are assigned at the epoch level and aggregated across all epochs of a patient to generate a final patientlevel prognosis. Five-fold patient-level cross-validation gives an area under the ROC curve of 0.861 ± 0.092, an accuracy of 0.774±0.045 and an F1 score of 0.733±0.057. Critically, specificity and precision are both 1.000 ± 0.000. Thus the model never predicts death for a child who survives, satisfying a stringent clinical safety requirement. Sensitivity is 0.581 ± 0.070, reflecting a deliberately conservative decision threshold.
Qualitative analyses offers tentative support for the physiological relevance of the learned features. t-SNE projections show clustering by patient identity and good separation between the two extreme EEG background patterns (continuous normal activity and electrocerebral silence) without supervision. Saliency analysis did not yield clinically interpretable patterns.
Compared to the leading feature-engineered qEEG baseline, the proposed approach achieves equivalent specificity and a slightly lower AUC, while removing the need for manual feature design and expert annotation. The modular architecture invites several extensions, including graph-based encoders that respect electrode topology, integration of auxiliary data such as ECG and clinical metadata, retrieval-based reasoning using large historical EEG archives, and more interpretable or end-to-end trainable models. Overall, this work demonstrates that contrastive learning can be effectively applied to raw pediatric EEG for conservative, label-efficient outcome prediction after cardiac arrest, and offers a mathematically grounded proof of concept for future clinical applications.
Downstream classification is performed with a k-nearest neighbors (k-NN) model. Probabilities are assigned at the epoch level and aggregated across all epochs of a patient to generate a final patientlevel prognosis. Five-fold patient-level cross-validation gives an area under the ROC curve of 0.861 ± 0.092, an accuracy of 0.774±0.045 and an F1 score of 0.733±0.057. Critically, specificity and precision are both 1.000 ± 0.000. Thus the model never predicts death for a child who survives, satisfying a stringent clinical safety requirement. Sensitivity is 0.581 ± 0.070, reflecting a deliberately conservative decision threshold.
Qualitative analyses offers tentative support for the physiological relevance of the learned features. t-SNE projections show clustering by patient identity and good separation between the two extreme EEG background patterns (continuous normal activity and electrocerebral silence) without supervision. Saliency analysis did not yield clinically interpretable patterns.
Compared to the leading feature-engineered qEEG baseline, the proposed approach achieves equivalent specificity and a slightly lower AUC, while removing the need for manual feature design and expert annotation. The modular architecture invites several extensions, including graph-based encoders that respect electrode topology, integration of auxiliary data such as ECG and clinical metadata, retrieval-based reasoning using large historical EEG archives, and more interpretable or end-to-end trainable models. Overall, this work demonstrates that contrastive learning can be effectively applied to raw pediatric EEG for conservative, label-efficient outcome prediction after cardiac arrest, and offers a mathematically grounded proof of concept for future clinical applications.
Retrospective analysis of PFIC data
Statistical modelling of disease trajectories and survival towards a better understanding of PFIC disease
Progressive familial intrahepatic cholestasis (PFIC) is a group of rare, inherited liver diseases that affect children and are characterised by impaired bile flow. Since PFIC is a paediatric ultra-rare disease, conducting randomised controlled trials is particularly challenging, making observational data essential for improving clinical management. This thesis analyses a large multinational observational retrospective data cohort with long-term follow-up of PFIC patients. The aim is to improve our understanding of PFIC and support more informed decision-making in patient care through the investigation of two key aspects of disease monitoring and progression. First, the thesis explores longitudinal trajectories of relevant biochemical parameters, serum bile acid levels and platelet counts, in patients with a specific subtype of PFIC, PFIC2, using latent class linear mixed models. This approach effectively identified distinct longitudinal patterns of serum bile acids and platelet counts in patients with PFIC2. These patterns highlight significant heterogeneity in the progression of laboratory parameters over time. Second, a comparative analysis of event-free survival is conducted between two European regional cohorts of PFIC patients, North-West Europe and South-Central Europe. Hypothesising that there are no differences in event-free survival of PFIC patients despite different care settings. This is achieved through a weighted survival analysis combining inverse probability treatment weighting with the Kaplan-Meier estimator and the Cox proportional hazards model. The results suggest there are no significant regional differences in event-free survival among PFIC2 patients between the two cohorts. Furthermore, a sensitivity analysis and permutation test have been performed, which also support this result. Together, these findings contribute to a more detailed understanding of disease progression in PFIC patients and provide practical tools and insights that can inform patient monitoring and clinical decision-making in the absence of randomised trials.
...
Progressive familial intrahepatic cholestasis (PFIC) is a group of rare, inherited liver diseases that affect children and are characterised by impaired bile flow. Since PFIC is a paediatric ultra-rare disease, conducting randomised controlled trials is particularly challenging, making observational data essential for improving clinical management. This thesis analyses a large multinational observational retrospective data cohort with long-term follow-up of PFIC patients. The aim is to improve our understanding of PFIC and support more informed decision-making in patient care through the investigation of two key aspects of disease monitoring and progression. First, the thesis explores longitudinal trajectories of relevant biochemical parameters, serum bile acid levels and platelet counts, in patients with a specific subtype of PFIC, PFIC2, using latent class linear mixed models. This approach effectively identified distinct longitudinal patterns of serum bile acids and platelet counts in patients with PFIC2. These patterns highlight significant heterogeneity in the progression of laboratory parameters over time. Second, a comparative analysis of event-free survival is conducted between two European regional cohorts of PFIC patients, North-West Europe and South-Central Europe. Hypothesising that there are no differences in event-free survival of PFIC patients despite different care settings. This is achieved through a weighted survival analysis combining inverse probability treatment weighting with the Kaplan-Meier estimator and the Cox proportional hazards model. The results suggest there are no significant regional differences in event-free survival among PFIC2 patients between the two cohorts. Furthermore, a sensitivity analysis and permutation test have been performed, which also support this result. Together, these findings contribute to a more detailed understanding of disease progression in PFIC patients and provide practical tools and insights that can inform patient monitoring and clinical decision-making in the absence of randomised trials.
Phylogenetics is the study of how species are related through evolution. These relationships are traditionally represented using branching diagrams called phylogenetic trees. However, certain evolutionary processes, such as hybridization or horizontal gene transfer, cannot be represented by trees alone. Therefore, phylogenetic networks - which allow additional connections between branches - are used to capture more complex evolutionary histories.
As phylogenetic networks become more complex, it becomes harder to determine whether a particular network can be uniquely reconstructed from observed DNA sequence data. This leads to the concept of identifiability. A network is said to be identifiable if, in theory, it can be uniquely determined from the data it generates. If two different networks produce the same data under a given evolutionary model, they are not identifiable from that data. Identifiability is essential for developing reconstruction methods that aim to infer evolutionary relationships from DNA.
This thesis investigates a specific class of phylogenetic networks, known as trinets. A trinet is a small sub-network that describes the evolutionary relationship between just three species. Trinets are useful building blocks for understanding and reconstructing larger phylogenetic networks. The main question studied in this work is whether these trinets are identifiable. We investigate whether specific types of trinets can be distinguished from simpler tree structures, using a mathematical approach based on phylogenetic invariants. These are special algebraic expressions that relate to the probabilities of observing certain DNA patterns. By evaluating such invariants, we may be able to detect whether the data came from a network or from a tree.
This thesis provides new insights into the identifiability of trinets. It shows that a specific type of trinet can be distinguished from a simple tree using an invariant. This is an important step toward understanding how more complex evolutionary networks can be identified from biological data from genes. ...
As phylogenetic networks become more complex, it becomes harder to determine whether a particular network can be uniquely reconstructed from observed DNA sequence data. This leads to the concept of identifiability. A network is said to be identifiable if, in theory, it can be uniquely determined from the data it generates. If two different networks produce the same data under a given evolutionary model, they are not identifiable from that data. Identifiability is essential for developing reconstruction methods that aim to infer evolutionary relationships from DNA.
This thesis investigates a specific class of phylogenetic networks, known as trinets. A trinet is a small sub-network that describes the evolutionary relationship between just three species. Trinets are useful building blocks for understanding and reconstructing larger phylogenetic networks. The main question studied in this work is whether these trinets are identifiable. We investigate whether specific types of trinets can be distinguished from simpler tree structures, using a mathematical approach based on phylogenetic invariants. These are special algebraic expressions that relate to the probabilities of observing certain DNA patterns. By evaluating such invariants, we may be able to detect whether the data came from a network or from a tree.
This thesis provides new insights into the identifiability of trinets. It shows that a specific type of trinet can be distinguished from a simple tree using an invariant. This is an important step toward understanding how more complex evolutionary networks can be identified from biological data from genes. ...
Phylogenetics is the study of how species are related through evolution. These relationships are traditionally represented using branching diagrams called phylogenetic trees. However, certain evolutionary processes, such as hybridization or horizontal gene transfer, cannot be represented by trees alone. Therefore, phylogenetic networks - which allow additional connections between branches - are used to capture more complex evolutionary histories.
As phylogenetic networks become more complex, it becomes harder to determine whether a particular network can be uniquely reconstructed from observed DNA sequence data. This leads to the concept of identifiability. A network is said to be identifiable if, in theory, it can be uniquely determined from the data it generates. If two different networks produce the same data under a given evolutionary model, they are not identifiable from that data. Identifiability is essential for developing reconstruction methods that aim to infer evolutionary relationships from DNA.
This thesis investigates a specific class of phylogenetic networks, known as trinets. A trinet is a small sub-network that describes the evolutionary relationship between just three species. Trinets are useful building blocks for understanding and reconstructing larger phylogenetic networks. The main question studied in this work is whether these trinets are identifiable. We investigate whether specific types of trinets can be distinguished from simpler tree structures, using a mathematical approach based on phylogenetic invariants. These are special algebraic expressions that relate to the probabilities of observing certain DNA patterns. By evaluating such invariants, we may be able to detect whether the data came from a network or from a tree.
This thesis provides new insights into the identifiability of trinets. It shows that a specific type of trinet can be distinguished from a simple tree using an invariant. This is an important step toward understanding how more complex evolutionary networks can be identified from biological data from genes.
As phylogenetic networks become more complex, it becomes harder to determine whether a particular network can be uniquely reconstructed from observed DNA sequence data. This leads to the concept of identifiability. A network is said to be identifiable if, in theory, it can be uniquely determined from the data it generates. If two different networks produce the same data under a given evolutionary model, they are not identifiable from that data. Identifiability is essential for developing reconstruction methods that aim to infer evolutionary relationships from DNA.
This thesis investigates a specific class of phylogenetic networks, known as trinets. A trinet is a small sub-network that describes the evolutionary relationship between just three species. Trinets are useful building blocks for understanding and reconstructing larger phylogenetic networks. The main question studied in this work is whether these trinets are identifiable. We investigate whether specific types of trinets can be distinguished from simpler tree structures, using a mathematical approach based on phylogenetic invariants. These are special algebraic expressions that relate to the probabilities of observing certain DNA patterns. By evaluating such invariants, we may be able to detect whether the data came from a network or from a tree.
This thesis provides new insights into the identifiability of trinets. It shows that a specific type of trinet can be distinguished from a simple tree using an invariant. This is an important step toward understanding how more complex evolutionary networks can be identified from biological data from genes.
This thesis investigates the use of neural networks for forecasting order volumes and introduces a framework that integrates these forecasts into route planning for B2B wholesale distributors. The proposed routing strategy features a two-stage optimization process: first, provisional routes are created based on predicted orders. Then, after actual orders are revealed, final routes are generated, taking the provisional plan into account.
A key operational challenge arises when the provisional and final routes differ. Customer orders assigned and sorted for delivery may need to be relocated, leading to increased manual handling. Since actual relocations are difficult to measure in simulations, this study defines a “swap” as the event where a customer is scheduled on a different route than initially planned. The main objective is to minimize these swaps while ensuring feasible and efficient delivery routes. This is achieved by improving forecasting accuracy and designing a framework to integrate forecasts into the routing process.
The research leverages ORTEC’s B2B Delivery software for route optimization, which allows preplanned routes as input but does not explicitly consider uncertainty. Various optimizer configurations and strategies are tested to assess their impact on swap reduction and route efficiency. For implementation, we propose a two-stage optimization strategy, which, due to limitations of the optimizer, includes two optimization rounds in the second stage. First, a full optimization is performed where customers from the provisional plan are fixed in their preplanned routes. This is followed by a light optimization round that encompasses all customers. In the light optimizer, raising the minimum estimated gain before attempting swaps had a more significant effect on reducing the number of swaps compared to increasing the number of swap attempts. Tests on forecasting qualities highlighted the importance of global metrics, such as the total number of customers and forecasted volume, on swap reduction and route efficiency.
Prior to this research, a proof of concept was conducted to forecast thousands of time series using traditional forecasting methods, which revealed two significant flaws. Firstly, the necessity to train separate forecasting models for individual time series resulted in the training of tens of thousands of models. Secondly, forecasting for new customers with limited historical data proved challenging. This motivated the adoption of neural network models as a unified solution, also capable of learning from similar patterns across multiple time series. This research tests three state-of-the-art neural network models: DeepAR from Amazon, Temporal Fusion Transformer (TFT) from Google, and N-HiTS from Nixtla. While all models struggled with the zero-inflated nature of order data, separating the prediction of order occurrence from order volume gave comparable or improved results to the traditional approach. The neural network models also show improvements in terms of forecasting for new customers. The main advantage lies in the ability to maintain just two models that function across all customers, eliminating the need for separate models for each customer.
DeepAR provided the most consistent results in route planning, despite a mean absolute error, likely due to superior global forecasting. TFT, while more accurate, led to more swaps due to systematic underestimation of the total volume. N-HiTS was the least effective but trained fastest.
Future research should explore improved loss functions of the neural network models and hierarchical forecasting. Incorporating stochastic optimization could further enhance the integration of forecasts into routing under uncertainty. ...
A key operational challenge arises when the provisional and final routes differ. Customer orders assigned and sorted for delivery may need to be relocated, leading to increased manual handling. Since actual relocations are difficult to measure in simulations, this study defines a “swap” as the event where a customer is scheduled on a different route than initially planned. The main objective is to minimize these swaps while ensuring feasible and efficient delivery routes. This is achieved by improving forecasting accuracy and designing a framework to integrate forecasts into the routing process.
The research leverages ORTEC’s B2B Delivery software for route optimization, which allows preplanned routes as input but does not explicitly consider uncertainty. Various optimizer configurations and strategies are tested to assess their impact on swap reduction and route efficiency. For implementation, we propose a two-stage optimization strategy, which, due to limitations of the optimizer, includes two optimization rounds in the second stage. First, a full optimization is performed where customers from the provisional plan are fixed in their preplanned routes. This is followed by a light optimization round that encompasses all customers. In the light optimizer, raising the minimum estimated gain before attempting swaps had a more significant effect on reducing the number of swaps compared to increasing the number of swap attempts. Tests on forecasting qualities highlighted the importance of global metrics, such as the total number of customers and forecasted volume, on swap reduction and route efficiency.
Prior to this research, a proof of concept was conducted to forecast thousands of time series using traditional forecasting methods, which revealed two significant flaws. Firstly, the necessity to train separate forecasting models for individual time series resulted in the training of tens of thousands of models. Secondly, forecasting for new customers with limited historical data proved challenging. This motivated the adoption of neural network models as a unified solution, also capable of learning from similar patterns across multiple time series. This research tests three state-of-the-art neural network models: DeepAR from Amazon, Temporal Fusion Transformer (TFT) from Google, and N-HiTS from Nixtla. While all models struggled with the zero-inflated nature of order data, separating the prediction of order occurrence from order volume gave comparable or improved results to the traditional approach. The neural network models also show improvements in terms of forecasting for new customers. The main advantage lies in the ability to maintain just two models that function across all customers, eliminating the need for separate models for each customer.
DeepAR provided the most consistent results in route planning, despite a mean absolute error, likely due to superior global forecasting. TFT, while more accurate, led to more swaps due to systematic underestimation of the total volume. N-HiTS was the least effective but trained fastest.
Future research should explore improved loss functions of the neural network models and hierarchical forecasting. Incorporating stochastic optimization could further enhance the integration of forecasts into routing under uncertainty. ...
This thesis investigates the use of neural networks for forecasting order volumes and introduces a framework that integrates these forecasts into route planning for B2B wholesale distributors. The proposed routing strategy features a two-stage optimization process: first, provisional routes are created based on predicted orders. Then, after actual orders are revealed, final routes are generated, taking the provisional plan into account.
A key operational challenge arises when the provisional and final routes differ. Customer orders assigned and sorted for delivery may need to be relocated, leading to increased manual handling. Since actual relocations are difficult to measure in simulations, this study defines a “swap” as the event where a customer is scheduled on a different route than initially planned. The main objective is to minimize these swaps while ensuring feasible and efficient delivery routes. This is achieved by improving forecasting accuracy and designing a framework to integrate forecasts into the routing process.
The research leverages ORTEC’s B2B Delivery software for route optimization, which allows preplanned routes as input but does not explicitly consider uncertainty. Various optimizer configurations and strategies are tested to assess their impact on swap reduction and route efficiency. For implementation, we propose a two-stage optimization strategy, which, due to limitations of the optimizer, includes two optimization rounds in the second stage. First, a full optimization is performed where customers from the provisional plan are fixed in their preplanned routes. This is followed by a light optimization round that encompasses all customers. In the light optimizer, raising the minimum estimated gain before attempting swaps had a more significant effect on reducing the number of swaps compared to increasing the number of swap attempts. Tests on forecasting qualities highlighted the importance of global metrics, such as the total number of customers and forecasted volume, on swap reduction and route efficiency.
Prior to this research, a proof of concept was conducted to forecast thousands of time series using traditional forecasting methods, which revealed two significant flaws. Firstly, the necessity to train separate forecasting models for individual time series resulted in the training of tens of thousands of models. Secondly, forecasting for new customers with limited historical data proved challenging. This motivated the adoption of neural network models as a unified solution, also capable of learning from similar patterns across multiple time series. This research tests three state-of-the-art neural network models: DeepAR from Amazon, Temporal Fusion Transformer (TFT) from Google, and N-HiTS from Nixtla. While all models struggled with the zero-inflated nature of order data, separating the prediction of order occurrence from order volume gave comparable or improved results to the traditional approach. The neural network models also show improvements in terms of forecasting for new customers. The main advantage lies in the ability to maintain just two models that function across all customers, eliminating the need for separate models for each customer.
DeepAR provided the most consistent results in route planning, despite a mean absolute error, likely due to superior global forecasting. TFT, while more accurate, led to more swaps due to systematic underestimation of the total volume. N-HiTS was the least effective but trained fastest.
Future research should explore improved loss functions of the neural network models and hierarchical forecasting. Incorporating stochastic optimization could further enhance the integration of forecasts into routing under uncertainty.
A key operational challenge arises when the provisional and final routes differ. Customer orders assigned and sorted for delivery may need to be relocated, leading to increased manual handling. Since actual relocations are difficult to measure in simulations, this study defines a “swap” as the event where a customer is scheduled on a different route than initially planned. The main objective is to minimize these swaps while ensuring feasible and efficient delivery routes. This is achieved by improving forecasting accuracy and designing a framework to integrate forecasts into the routing process.
The research leverages ORTEC’s B2B Delivery software for route optimization, which allows preplanned routes as input but does not explicitly consider uncertainty. Various optimizer configurations and strategies are tested to assess their impact on swap reduction and route efficiency. For implementation, we propose a two-stage optimization strategy, which, due to limitations of the optimizer, includes two optimization rounds in the second stage. First, a full optimization is performed where customers from the provisional plan are fixed in their preplanned routes. This is followed by a light optimization round that encompasses all customers. In the light optimizer, raising the minimum estimated gain before attempting swaps had a more significant effect on reducing the number of swaps compared to increasing the number of swap attempts. Tests on forecasting qualities highlighted the importance of global metrics, such as the total number of customers and forecasted volume, on swap reduction and route efficiency.
Prior to this research, a proof of concept was conducted to forecast thousands of time series using traditional forecasting methods, which revealed two significant flaws. Firstly, the necessity to train separate forecasting models for individual time series resulted in the training of tens of thousands of models. Secondly, forecasting for new customers with limited historical data proved challenging. This motivated the adoption of neural network models as a unified solution, also capable of learning from similar patterns across multiple time series. This research tests three state-of-the-art neural network models: DeepAR from Amazon, Temporal Fusion Transformer (TFT) from Google, and N-HiTS from Nixtla. While all models struggled with the zero-inflated nature of order data, separating the prediction of order occurrence from order volume gave comparable or improved results to the traditional approach. The neural network models also show improvements in terms of forecasting for new customers. The main advantage lies in the ability to maintain just two models that function across all customers, eliminating the need for separate models for each customer.
DeepAR provided the most consistent results in route planning, despite a mean absolute error, likely due to superior global forecasting. TFT, while more accurate, led to more swaps due to systematic underestimation of the total volume. N-HiTS was the least effective but trained fastest.
Future research should explore improved loss functions of the neural network models and hierarchical forecasting. Incorporating stochastic optimization could further enhance the integration of forecasts into routing under uncertainty.
Efficient staff scheduling is crucial for smooth baggage handling at Schiphol Airport. Each day, KLM must allocate hundreds of employees to hundreds of time-sensitive loading and unloading tasks. Even small disruptions, such as flight delays or staff shortages, can quickly lead to infeasible schedules and unhandled flights. This thesis develops an optimization framework to provide more insight into the robustness of KLM’s day-ahead baggage handling schedule.
The problem is modeled as a Vehicle Routing Problem with Time Windows (VRPTW), extended mode selection, travel times, and mandatory breaks. To handle the model’s complexity, a Fix-and-Optimize approach is applied, iteratively optimizing subsets of the problem while keeping others fixed. Two extensions are introduced to improve task coverage: allowing staff to assist across work areas (cross-zone assignments) and slightly delaying flights (postponements) when necessary.
Scenario analyses evaluate how disruptions, flight delays and staff shortages, affect task coverage. Results based on real KLM data show that the Base Model already increases the number of planned tasks compared to the current planning tool when comparing optimization for a full shift. Allowing postponements further improves coverage, often enabling full task completion. Under disruptions, the model identifies critical time periods and areas where additional flexibility or actions are required.
This research combines mathematical modeling and analysis to better understand the structure and resilience of KLM’s daily planning. The proposed approach highlights where schedules are vulnerable and demonstrates how optimization can support planners in preparing for operational uncertainty. ...
The problem is modeled as a Vehicle Routing Problem with Time Windows (VRPTW), extended mode selection, travel times, and mandatory breaks. To handle the model’s complexity, a Fix-and-Optimize approach is applied, iteratively optimizing subsets of the problem while keeping others fixed. Two extensions are introduced to improve task coverage: allowing staff to assist across work areas (cross-zone assignments) and slightly delaying flights (postponements) when necessary.
Scenario analyses evaluate how disruptions, flight delays and staff shortages, affect task coverage. Results based on real KLM data show that the Base Model already increases the number of planned tasks compared to the current planning tool when comparing optimization for a full shift. Allowing postponements further improves coverage, often enabling full task completion. Under disruptions, the model identifies critical time periods and areas where additional flexibility or actions are required.
This research combines mathematical modeling and analysis to better understand the structure and resilience of KLM’s daily planning. The proposed approach highlights where schedules are vulnerable and demonstrates how optimization can support planners in preparing for operational uncertainty. ...
Efficient staff scheduling is crucial for smooth baggage handling at Schiphol Airport. Each day, KLM must allocate hundreds of employees to hundreds of time-sensitive loading and unloading tasks. Even small disruptions, such as flight delays or staff shortages, can quickly lead to infeasible schedules and unhandled flights. This thesis develops an optimization framework to provide more insight into the robustness of KLM’s day-ahead baggage handling schedule.
The problem is modeled as a Vehicle Routing Problem with Time Windows (VRPTW), extended mode selection, travel times, and mandatory breaks. To handle the model’s complexity, a Fix-and-Optimize approach is applied, iteratively optimizing subsets of the problem while keeping others fixed. Two extensions are introduced to improve task coverage: allowing staff to assist across work areas (cross-zone assignments) and slightly delaying flights (postponements) when necessary.
Scenario analyses evaluate how disruptions, flight delays and staff shortages, affect task coverage. Results based on real KLM data show that the Base Model already increases the number of planned tasks compared to the current planning tool when comparing optimization for a full shift. Allowing postponements further improves coverage, often enabling full task completion. Under disruptions, the model identifies critical time periods and areas where additional flexibility or actions are required.
This research combines mathematical modeling and analysis to better understand the structure and resilience of KLM’s daily planning. The proposed approach highlights where schedules are vulnerable and demonstrates how optimization can support planners in preparing for operational uncertainty.
The problem is modeled as a Vehicle Routing Problem with Time Windows (VRPTW), extended mode selection, travel times, and mandatory breaks. To handle the model’s complexity, a Fix-and-Optimize approach is applied, iteratively optimizing subsets of the problem while keeping others fixed. Two extensions are introduced to improve task coverage: allowing staff to assist across work areas (cross-zone assignments) and slightly delaying flights (postponements) when necessary.
Scenario analyses evaluate how disruptions, flight delays and staff shortages, affect task coverage. Results based on real KLM data show that the Base Model already increases the number of planned tasks compared to the current planning tool when comparing optimization for a full shift. Allowing postponements further improves coverage, often enabling full task completion. Under disruptions, the model identifies critical time periods and areas where additional flexibility or actions are required.
This research combines mathematical modeling and analysis to better understand the structure and resilience of KLM’s daily planning. The proposed approach highlights where schedules are vulnerable and demonstrates how optimization can support planners in preparing for operational uncertainty.
Proximal Causal Inference
Adjusting for the Unobserved
Causal relationships are at the heart of the scientific method. The causal revolution of the 21st century has opened the doors for many new approaches to quantify such relationships. In this thesis, we study the novel framework of proximal causal inference, which enables estimation of causal parameters even in the presence of unmeasured confounders, overcoming the limitations imposed by the Conditional Exchangeability assumption of the classic causal framework. In particular, we shall focus on determining and estimating the Causal Exposure Response Function (CERF) under this new set of assumptions. First, we introduce the problem and present a literature review of existing approaches to estimate bridge functions; then, we show theoretical results for extensions of classic linear results and a novel quasi- Bayesian method. This is then completed by showcasing performance on many simulated numerical examples and two real-world problems: Sustainable Causal Investing, and the effect of exercise on sleep.
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Causal relationships are at the heart of the scientific method. The causal revolution of the 21st century has opened the doors for many new approaches to quantify such relationships. In this thesis, we study the novel framework of proximal causal inference, which enables estimation of causal parameters even in the presence of unmeasured confounders, overcoming the limitations imposed by the Conditional Exchangeability assumption of the classic causal framework. In particular, we shall focus on determining and estimating the Causal Exposure Response Function (CERF) under this new set of assumptions. First, we introduce the problem and present a literature review of existing approaches to estimate bridge functions; then, we show theoretical results for extensions of classic linear results and a novel quasi- Bayesian method. This is then completed by showcasing performance on many simulated numerical examples and two real-world problems: Sustainable Causal Investing, and the effect of exercise on sleep.
Distributional Regression
Estimation of Conditional Distributions with Likelihood Ratio Order Constraint
This thesis aims to estimate conditional distribution functions subject to the likelihood ratio order constraint. We use the modified gradient projection method to ensure that in each iteration, the point stays feasible while improving the objective function. Regarding the objective function, we use the continuous ranked probability score (CRPS), a loss function used for forecast evaluation. Given its strict propriety, we use it for estimation procedures. Our numerical experiments indicate that the estimated conditional distribution functions perform reasonably well as the number of iteration increases. However, the algorithm’s long running time makes it impractical for use in practice. Furthermore, due to the reparametrization of the estimand, the objective function loses its convexity property while the feasible set is convex. This causes the algorithm to potentially return a local minimum, rather than a global minimum.
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This thesis aims to estimate conditional distribution functions subject to the likelihood ratio order constraint. We use the modified gradient projection method to ensure that in each iteration, the point stays feasible while improving the objective function. Regarding the objective function, we use the continuous ranked probability score (CRPS), a loss function used for forecast evaluation. Given its strict propriety, we use it for estimation procedures. Our numerical experiments indicate that the estimated conditional distribution functions perform reasonably well as the number of iteration increases. However, the algorithm’s long running time makes it impractical for use in practice. Furthermore, due to the reparametrization of the estimand, the objective function loses its convexity property while the feasible set is convex. This causes the algorithm to potentially return a local minimum, rather than a global minimum.
Authorship attribution is the task of determining the unknown author of a text. In forensic authorship attribution, the likelihood that a suspect has written a specific text of unknown origin is computed based on reference texts from both the suspect and a background population. The current method used at the Netherlands Forensic Institute contains a manual and a computational part. In this thesis, we attempted to improve the computational part of this process. We study this problem from three directions.
Firstly, the performance of state-of-the-art computational authorship attribution methods was assessed on Dutch, forensically relevant corpora. The compared methods were support vector machines combined with masking, using either word or character n-grams as features, BERT-based models using a mean pooling strategy to handle long texts and the baseline, which consists of a logistic regression model with the 100 most frequent Dutch words as features. We notice similar performance differences between state-of-the-art methods as in the literature. The best-performing method was a support vector machine without masking using character n-grams as features. In comparison, both the baseline and BERT-based models perform worse on our corpora.
Secondly, a score-based likelihood ratio system was created to modify the computational authorship attribution methods for usage in forensics. This method is based on kernel density estimators and uses cross-calibration to handle the small number of training and calibration texts of the suspect. For most methods, the performance is in line with the previous performances outside the likelihood ratio system, except for the BERT-based methods, which significantly underperform when part of a likelihood ratio system. This is likely caused by the combination of cross-calibration and the randomness in finetuning BERT models.
Additionally, authorship attribution methods should be topic-robust, such that their attribution is not biased by the topic of a text. We introduced two new metrics to measure the topic-robustness of authorship attribution methods, ‘topic impact’ and ‘conversation impact’. These metrics can only be used on specific types of corpora, the topic impact can be computed on topic-controlled corpora and the conversation impact can be computed on conversational corpora. To study whether these metrics both measured the topic-robustness of authorship attribution methods for their respective corpus type, we computed the correlation between the results of the metrics for varying authorship attribution methods.
We found a correlation of 0.68. As a result, we cannot conclude that the conversation impact is a perfect metric to measure the topic-robustness of methods using conversational corpora, but it does give a good indication of large differences between methods.
Using this new metric, we found that our best-performing methods suffered from a high conversation impact and, as a result, might be more likely to have a low topic-robustness. If more of the infrequent words were masked, the conversation impact decreased, but so did the performance. A trade-off between high performance and high topic-robustness must be made when a model is chosen for real forensic case work. The conversation impact metric we proposed can help quantify these effects on forensically relevant corpora and therefore assist in making better choices.
...
Firstly, the performance of state-of-the-art computational authorship attribution methods was assessed on Dutch, forensically relevant corpora. The compared methods were support vector machines combined with masking, using either word or character n-grams as features, BERT-based models using a mean pooling strategy to handle long texts and the baseline, which consists of a logistic regression model with the 100 most frequent Dutch words as features. We notice similar performance differences between state-of-the-art methods as in the literature. The best-performing method was a support vector machine without masking using character n-grams as features. In comparison, both the baseline and BERT-based models perform worse on our corpora.
Secondly, a score-based likelihood ratio system was created to modify the computational authorship attribution methods for usage in forensics. This method is based on kernel density estimators and uses cross-calibration to handle the small number of training and calibration texts of the suspect. For most methods, the performance is in line with the previous performances outside the likelihood ratio system, except for the BERT-based methods, which significantly underperform when part of a likelihood ratio system. This is likely caused by the combination of cross-calibration and the randomness in finetuning BERT models.
Additionally, authorship attribution methods should be topic-robust, such that their attribution is not biased by the topic of a text. We introduced two new metrics to measure the topic-robustness of authorship attribution methods, ‘topic impact’ and ‘conversation impact’. These metrics can only be used on specific types of corpora, the topic impact can be computed on topic-controlled corpora and the conversation impact can be computed on conversational corpora. To study whether these metrics both measured the topic-robustness of authorship attribution methods for their respective corpus type, we computed the correlation between the results of the metrics for varying authorship attribution methods.
We found a correlation of 0.68. As a result, we cannot conclude that the conversation impact is a perfect metric to measure the topic-robustness of methods using conversational corpora, but it does give a good indication of large differences between methods.
Using this new metric, we found that our best-performing methods suffered from a high conversation impact and, as a result, might be more likely to have a low topic-robustness. If more of the infrequent words were masked, the conversation impact decreased, but so did the performance. A trade-off between high performance and high topic-robustness must be made when a model is chosen for real forensic case work. The conversation impact metric we proposed can help quantify these effects on forensically relevant corpora and therefore assist in making better choices.
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Authorship attribution is the task of determining the unknown author of a text. In forensic authorship attribution, the likelihood that a suspect has written a specific text of unknown origin is computed based on reference texts from both the suspect and a background population. The current method used at the Netherlands Forensic Institute contains a manual and a computational part. In this thesis, we attempted to improve the computational part of this process. We study this problem from three directions.
Firstly, the performance of state-of-the-art computational authorship attribution methods was assessed on Dutch, forensically relevant corpora. The compared methods were support vector machines combined with masking, using either word or character n-grams as features, BERT-based models using a mean pooling strategy to handle long texts and the baseline, which consists of a logistic regression model with the 100 most frequent Dutch words as features. We notice similar performance differences between state-of-the-art methods as in the literature. The best-performing method was a support vector machine without masking using character n-grams as features. In comparison, both the baseline and BERT-based models perform worse on our corpora.
Secondly, a score-based likelihood ratio system was created to modify the computational authorship attribution methods for usage in forensics. This method is based on kernel density estimators and uses cross-calibration to handle the small number of training and calibration texts of the suspect. For most methods, the performance is in line with the previous performances outside the likelihood ratio system, except for the BERT-based methods, which significantly underperform when part of a likelihood ratio system. This is likely caused by the combination of cross-calibration and the randomness in finetuning BERT models.
Additionally, authorship attribution methods should be topic-robust, such that their attribution is not biased by the topic of a text. We introduced two new metrics to measure the topic-robustness of authorship attribution methods, ‘topic impact’ and ‘conversation impact’. These metrics can only be used on specific types of corpora, the topic impact can be computed on topic-controlled corpora and the conversation impact can be computed on conversational corpora. To study whether these metrics both measured the topic-robustness of authorship attribution methods for their respective corpus type, we computed the correlation between the results of the metrics for varying authorship attribution methods.
We found a correlation of 0.68. As a result, we cannot conclude that the conversation impact is a perfect metric to measure the topic-robustness of methods using conversational corpora, but it does give a good indication of large differences between methods.
Using this new metric, we found that our best-performing methods suffered from a high conversation impact and, as a result, might be more likely to have a low topic-robustness. If more of the infrequent words were masked, the conversation impact decreased, but so did the performance. A trade-off between high performance and high topic-robustness must be made when a model is chosen for real forensic case work. The conversation impact metric we proposed can help quantify these effects on forensically relevant corpora and therefore assist in making better choices.
Firstly, the performance of state-of-the-art computational authorship attribution methods was assessed on Dutch, forensically relevant corpora. The compared methods were support vector machines combined with masking, using either word or character n-grams as features, BERT-based models using a mean pooling strategy to handle long texts and the baseline, which consists of a logistic regression model with the 100 most frequent Dutch words as features. We notice similar performance differences between state-of-the-art methods as in the literature. The best-performing method was a support vector machine without masking using character n-grams as features. In comparison, both the baseline and BERT-based models perform worse on our corpora.
Secondly, a score-based likelihood ratio system was created to modify the computational authorship attribution methods for usage in forensics. This method is based on kernel density estimators and uses cross-calibration to handle the small number of training and calibration texts of the suspect. For most methods, the performance is in line with the previous performances outside the likelihood ratio system, except for the BERT-based methods, which significantly underperform when part of a likelihood ratio system. This is likely caused by the combination of cross-calibration and the randomness in finetuning BERT models.
Additionally, authorship attribution methods should be topic-robust, such that their attribution is not biased by the topic of a text. We introduced two new metrics to measure the topic-robustness of authorship attribution methods, ‘topic impact’ and ‘conversation impact’. These metrics can only be used on specific types of corpora, the topic impact can be computed on topic-controlled corpora and the conversation impact can be computed on conversational corpora. To study whether these metrics both measured the topic-robustness of authorship attribution methods for their respective corpus type, we computed the correlation between the results of the metrics for varying authorship attribution methods.
We found a correlation of 0.68. As a result, we cannot conclude that the conversation impact is a perfect metric to measure the topic-robustness of methods using conversational corpora, but it does give a good indication of large differences between methods.
Using this new metric, we found that our best-performing methods suffered from a high conversation impact and, as a result, might be more likely to have a low topic-robustness. If more of the infrequent words were masked, the conversation impact decreased, but so did the performance. A trade-off between high performance and high topic-robustness must be made when a model is chosen for real forensic case work. The conversation impact metric we proposed can help quantify these effects on forensically relevant corpora and therefore assist in making better choices.