Large infrastructure development projects, such as airports, are significantly affected by the uncertainties in the geographic and socio-economic environment. Especially in the early stages of the project, little information about the final specifics of a project is available. As a result, accurately predicting the cost of such a project, as well as its financial feasibility, becomes a complex matter.
This thesis aims to develop a methodology framework, which can support the financial decision-making process in the early stages of airport development projects through an interactive tool. The methodology aims to use Structured Expert Judgment (SEJ) and Bayesian Network (BN) characteristics to provide insight into uncertainties surrounding airport development and its corresponding costs.
Two types of uncertainty are found to directly contribute to the financial risk associated with investment in infrastructure development, based on literature. One type pertains to the technical requirements for airfield pavements. The other type of uncertainty relates to price differences due to fluctuations and inflation.
The airfield pavements (the runway, taxiway, and apron) were determined to be the critical elements in cost estimation. Their dimensions and square meter prices were covered in a SEJ study to obtain probability distributions for these variables. The probability distributions were then combined with rank correlation coefficients calculated from a database with reference airports to implement in a Non-Parametric BN (NPBN).
The result of the research is a Graphical User Interface (GUI): DAiCE. This GUI enables the conditionalisation of the NPBN, predicting pavement dimensions and associated costs through simulation. The tool allows for input of project requirements and analysis of the project’s financial outlook.
DAiCE is proven to produce statistically significant results for airfield design issues. The simulated design values and cost estimates obtained from the tool are in line with those retrieved from reference projects. Though the tool is still bound to some limitations, such the included structures and exploitation models, it is concluded that the model of the airfield design landscape and its implementation in DAiCE can be used to support claims regarding the financial feasibility of an airport development project.
This thesis formulates several recommendations for future research, which are specified for SEJ, the construction and application of BNs, and further development of DAiCE. For SEJ, this includes investigation into different aggregation methods for SEJ, diversification of the expert pool, and expansion of the elicited topics. In addition, it is recommended to further develop the used software for constructing BNs, verification of model parameters, and exploring applicability of BNs in other research fields. Finally, expansion of the developed model, and additional functionalities for DAiCE are proposed.

We consider a subset of simple proving exercises that are part of the Lean 4 tutorials. The exercises consist of a statement, and the task will consist of creating a proof term of the desired type through the use of tactics.
Large Language Models on their own are known to be able to produce syntactically correct pieces of text but are unable to come up with semantically correct pieces of text once very similar solutions are lacking in the dataset it was trained on.
This work reviews the Sequential Monte Carlo with Expectation-Maximization (SMX) algorithm for general reinforcement learning problems, and applies it to theorem proving using LLMs.
This work shows that the SMX algorithm is applicable to tasks where formal verification can be performed on the output, allowing the calculated reward to steer the reasoning process.
We furthermore formally prove a theorem that will be important in showing that the resampling step in SMX is necessary to mitigate sample impoverishment.
The theoretical part of this thesis builds on the theory of the SMX paper by verifying the derivation of the E-step, starting from the Evidence Lower Bound (ELBO). This derivation was missing from the original SMX paper.

Bayesian Networks (BNs) are popular models that represent complex relationships between variables, which can be quantified by Conditional Probability Tables (CPTs) in the discrete case. If data are not sufficient, experts can be involved to assess the probabilities in the CPTs through Structured Expert Judgment (SEJ), which is often a burdensome task. To lighten the elicitation burden, several methods have been developed previously to construct CPTs using a limited number of input parameters, such as the Ranked Nodes Method (RNM), InterBeta and Functional Interpolation. These methods are first analyzed theoretically, where limitations and potential improvements are determined, which were used as inspiration to develop extensions to the methods. The methods and newly developed extensions, including "ExtraBeta" and "AutoRNM", were applied to reconstruct fully elicited CPTs. Finally, simulation studies are performed to find best practices for InterBeta. InterBeta with parent weights is determined as the best-performingmethod, and the AutoRNM and ExtraBeta extensions are worth exploring further.

We have studied the predictability of the complications after bowel surgery with the dataset provided by the MST.We see that the correlated data and rare event outcomes lead to the modest performance of the models employed. We have done an extensive preprocessing where we went from a total of 375 variables to 51 explanatory variables. We applied 3 variable selection methods to predict severe complications and any complications in 3 different scenarios (before surgery, right after surgery, and after primary stay). We will see that interoperative variables add valuable information (comparing Scenario 1 with Scenario 2). However, the interoperative variables become less important for predicting the complications post-primary stay (in Scenario 3). Generally, the most important variables are general health scores (WHO score and ASA class) except when predicting complications right after surgery then interoperative variables, for example blood loss, seem to contribute more to complications than variables indicating preoperative health. We will see that post-operative variables are selected for modelling complications after the primary hospital stay, but that these models do not perform adequately since not many complications are present after primary hospital stay. We compared a literature based selection, one resulting from performing marginal testing and an AIC forward variable selection. We see that in the literature many variables are considered important. Sadly we did not extract information about the timing or severity of the complications from the literature. The AIC forward seems prone to select correlated variables which often led to the resulting model to overfit. The marginal importance was more restrictive than the literature model. We have seen that the (unweighted) logistic regression severely underestimates the outcomes and that the weighted logistic regression will lead to a more informative model but with more misclassifications. We included the Threat score (TS) and the Matthews correlation coefficient (MCC) in our validation and confirmed that these are valid measures for scoring the performace of models with a rare outcome.

At crime scenes, various methods can be used to determine how much time has passed since the act happened, for example a body left at the scene, camera footage or eye witnesses. In this thesis, however, a different method shall be used to determine the time of the crime. The time will be determined using blood evidence.

To be exact, the goal of this thesis is to analyse the aging of bloodstains through colour analysis, and constructing a Bayesian network (BN) which can accurately make predictions on the time of deposition of a bloodstain.

The data used for the construction of the BNs was obtained from images provided by the Leiden Institute of Physics (LION). To obtain the data, the bloodstains in the images first need to be isolated from the background. Afterwards, the bloodstains are split into two parts: the inner part of the bloodstain and the complete bloodstain. Both the isolation and the splitting are done using a method called masking. Afterwards they can be converted to RGB (red, green, blue) values and using these RGB values, the following data can be collected for each colour channel of both the inner part of the bloodstain and the whole bloodstain: mean, min, max, variance, and the 5%, 20%, 50%, 80% and 95% quantiles.

Using various subsets of the data, BNs can be constructed. The structure of the BN is determined using a structure-learning algorithm called hill-climbing . To determine the validity of a given structure k-fold cross-validation can be performed using a given loss function. In this thesis, k=5 has been used, and the Mean Squared Error (MSE) has been taken as the loss function. Upon comparison of the MSE, it seems that the best model is given by the red values of a bloodstain. However, even the best performing model found in this thesis still has a considerably poor performance as the BN for the red variables has an MSE of 15149.81.

During this bachelorproject, more research is done to investigate the properties of the Hanea’s and Nane’s calibration score and to look at slight adjustment of Hanea’s and Nane’s calibration score. Both simulated data and real data will be used to investigate the behaviour of these calibration scores.

Out of Home advertising is traditional outdoor advertising. Over the last decade the digital Out of Home advertising possibilities have grown substantially. These possibilities include hour-based advertisement schedules, rapidly implemented changes to advertisements and obtaining location data from consumers being exposed to advertisements. Investigating these possibilities further for improving customer engagement and optimising target group reach is of great importance in marketing and marketing science. This thesis will focus on exposure data obtained from vehicle locations in central London. Using this data we want to model the frequency with which individuals see advertisements and research the overlap in exposures of individuals to multiple media vehicles where advertisements are displayed. We focus on modelling exposures of individuals to two vehicles, comparing different types of bivariate distributions. In this thesis we present the comparison of two models: an adapted version of the Sarmanov bivariate distribution and copulas. We refer to these models as the Danaher and Copula model respectively.

The fitting and simulations of the models are based on bivariate data of two specified vehicles, to be able to comment on the overlap between these vehicles. To investigate the performance of the models all combinations of vehicles are modelled after which the results are combined. Both models simulate small frequencies of exposures of individuals adequate, but for more extreme values both models fail to represent the observed data. Especially the simulation of overlap is done poorly by the models. Several approaches have been tried to improve the models' performance, without much success. The analysis shows that the data at hand requires more sophisticated methods to handle joint exposure and more research needs to be done.

In addition the variable distance is added to the research problem, which intuitively has great influence on the overlap between media vehicles. This is done by using 3-dimensional copulas. For this research we modify the data: instead of first fitting and simulating a copula model on the data of two vehicles and then combining the results of all vehicle combinations, we first combine the data from all the combinations of vehicles and repeat the fitting procedure thereafter. Several options for the modelling of these copulas are presented. Similar analysis shows, again, that the nature of the data requires more complex models to handle the overlap while also accounting for the vehicle distance. Finally, using the modified data we look back at the 2-dimensional copula model and perceive an excellent resemblance of the data for the Student-t copula.

In the process of drilling wells to produce hydrocarbons, an exploration strategy is used to determine which wells should be drilled and in which order. This strategy is vital, as a suboptimal drilling sequence will lead to more expenses and fewer gains.
Furthermore, the wells considered in most exploration strategies are geologically
dependent. Thus, a realistic model of these dependencies will be beneficial and
contribute to a more reliable optimal drilling strategy.
Previous research has shown that modelling similarities between the geological
properties of prospect wells in the same region and updating the drilling strategy dynamically after more information is available can add much value. However, the currently developed models are not realistic enough to use in practice. Previous models separated the process into two parts, first modelling the geological success with deterministic rewards and then applying dynamic programming to obtain the sequential drilling strategy.
This thesis proposes a new model with the addition of flexible uncertainty and
dependency models between the geological characteristics in the hydrocarbon volume calculation of a reservoir. For this purpose, non-parametric Bayesian networks in combination with copulae are used. This model and the input format of the required data align with how data is gathered in the oil and gas industry. The dependencies are modelled based on simple expert assessments.
After the new model for the geological properties of prospect wells and their dependencies is constructed, a decision policy that hinges on the observations of previously drilled wells is constructed. Previously used dynamic programming becomes infeasible with continuous variables and with a large number of wells. Therefore, the reinforcement learning algorithm Q-learning is used, which is better equipped to handle these more complex models.
The analysis shows that Q-learning achieves similar results to dynamic programming. Afterwards, the new model is applied to a case based on real oil and gas industry data. The results show that this case does not lend itself to an improvement when the drilling strategy is sequentially updated as the decisions compared to the original drilling strategy did not change. This occurs because the prospects all have high positive expected rewards and should be drilled, regardless of the other wells’ outcomes and dependencies.
Another case with synthetic data is explored with more favourable characteristics
that, in theory, should lead to the result of the policy from the new model and Qlearning outperforming the current industry policy. However, this was not shown yet within the time constraints of this thesis, as the Q-learner should be run for a more extended period and tuned according to the case.
While the model is created for dynamic sequential decision making in the application of drilling wells, this method can easily be adapted to fit any other application where decisions should be updated sequentially, and the
dependencies can be modelled through a Bayesian network.
In conclusion, the key contributions of this thesis are the creation of a new model for the dependencies between geological properties of a hydrocarbon reservoir and the use of the Q-learning reinforcement learning algorithm to compute the sequentially updated drilling strategy as an alternative to dynamic programming.

In this thesis, we explore a proposal from Stedin that advocates heating the city of Stad aan `t Haringvliet with hydrogen rather than natural gas. Switching from natural gas to hydrogen presents plenty of unknown factors which must be properly evaluated for an accurate and realistic risk picture, including the danger of running out of hydrogen. The objective of this study is to examine the security of a 100% hydrogen supply in city buildings. For this MSc thesis, the security of supply is defined as a reliable and uninterrupted supply of hydrogen for heating purposes. We explore the security of supply by evaluating the risk to it.

To achieve this goal, we construct a hydrogen supply system using Stedin's criteria. The Classical Model for Structured Expert Judgement and the Bayesian Network are the two mathematical techniques we use to evaluate the risks. The lack of acceptable data makes the task of quantifying the risk to supply much more difficult in this regard. Expert opinion remains the sole trustworthy source of information in these conditions for quantifying uncertainty. However, expert opinion should be validated using objective performance measures. As a result, we adopt the Classical Model for Structured Expert Judgement. The resulting uncertainty distributions of the Structured Expert Judgement research are then integrated into a Bayesian Network that models the uncertainty within the hydrogen supply system. Bayesian Networks are an effective tool for visualizing a domain's probabilistic model, examining all random variable interactions, and inferring probability for scenarios based on available data.\\

The findings of Structured Expert Judgment reveal that there will be a forecast of 114 minutes of not enough hydrogen in the buildings of Stad aan 't Haringvliet in the first year of realizing Stedin's pilot, given the event that there will be a lack of hydrogen in Stad aan `t Haringvliet. Moreover, the security of supply is expected to not be achieved with an estimated probability of 0.06839 for the first year of realizing this pilot. Furthermore, failure rates for each component of the hydrogen supply system have also been quantified using the Classical Model, and one or more mitigations have been proposed for each component. Quantifying the Bayesian Network with the distributions for each component of the hydrogen supply system that resulted from the expert judgment study, yields distinct results than experts' aggregated distributions on the estimated probability and the duration of not meeting the energy demand. The results show that the best-estimated probability for not having enough hydrogen in the buildings equals 0.2067 and when we consider the event of having a lack of hydrogen in the buildings, the best estimated time for how long this will last equals 3.135 minutes in the first year of realizing Stedin's pilot.

Electricity is a quite unique commodity. Due to the economically non-storable nature of the commodity that electricity is, the constant balance between consumption and production, weather effects, such as temperature, wind speed, solar intensity etc, and the intensity of everyday and business activities, e.g. holi- days, weekends, on- and off-peak hours etc., the price dynamics of this commodity are quite unique as they are not observed in any other market. This extreme price volatility has forced market participants to hedge volumes as well as price risks. Naturally, electricity price forecast models are of great interest to portfolio managers.
Current data-driven models are combined with expertise of traders due to the considerable uncertainty of these models. We aim to subject trader expertise to a transparent methodology using structured expert judgement. During this study, we conduct two elicitations whose variables of interest concern average day- ahead spot prices for 2025, 2030 and 2035. We distinguish between baseload and peakload price. The first elicitation uses assessments regarding current Dutch day-ahead electricity spot prices to forecast forecast the variables of interest. We forecast the average day-ahead electricity spot price for 2025, 2030 and 2035. The second elicitation uses assessments regarding data on past, current and future developments in the Dutch electricity markets to forecast forecast the variables of interest. The second elicitation results in a decision maker with a higher price forecast than the decision maker of the first elicitation. Uncertainty regarding the forecast is higher for 2025 and 2030 during the second study. Uncertainty is equally high regarding the peakload price forecast for 2035 in both studies, however the range shifts.

In this thesis the differences in performance scores of experts in the Classical Model for structured expert judgement are analyzed. The underlying assumption in the Classical Model is that variance in performances of experts in a panel is at least partly resultant of the expert's ability to quantify uncertainty. This assumption is tested against the so called Random Expert Hypothesis, that states that these differences are solely resultant of random fluctuations. At the five percent significance level it is concluded that the variation in the combined score of experts cannot exclusively be explained by random fluctuations. When the assumption is tested individually for three different subject fields, health, policy and science, the Random Expert Hypothesis cannot be rejected for both health and policy related studies. Lastly it is shown that the variation in performances between the best and worst expert in a panel strongly correlates with the performance of the best expert against random panels. This indicates that the aggregation of experts according to the scoring rule in the Classical Model may primarily work to diminish the influence of low performing experts.

Applying multiple structure learning algorithms like hill-climbing, incremental association and grow-shrink, to investigate their robustness, predictive capabiliy and goodness of fit on multiple discrete Bayesian networks and Gaussian Bayesian networks.

Elections polls have been known to exist since 1824 [14], to fulfill the objective of what is happening and may happen. In this thesis it is investigated what the performance of election polls is and if the aggregation of polls give a better forecast than the polls themselves. The data is used of Spain during years 2012 until 2017 and The Netherlands during years 2010 until 2021. Furthermore, in this thesis the results of Spain and The Netherlands are compared. The aggregation of polls is done by using The Classical Model of Roger Cooke [2] and by using two types of Equal weighting. When using the Classical Model two different methods are used, namely a window-shift way and a cumulative way. The comparison between the aggregation of polls and the polls themselves is done by looking at the unnormalized weights and the total absolute differences. The results were quite different for the two countries. However, for both countries it appeared that method 1 was better when looking at the unnormalized weights, while method 2 was better when considering the total absolute differences. When looking at the unnormalized weights for the Spanish data the forecast when aggregating the polls, using the Item weight decision maker, was better than most of the polls’ forecasts. In addition when looking at the absolute total differences of the Spanish data, the forecast when aggregating the polls, also using the Item weight decision maker, was better than most of the polls’ forecasts. Similarly for the Dutch data when looking at the unnormalized weights, the forecast of the election when aggregating the polls, using the Performance-based decision maker, was better than most of the polls’ forecasts. In addition, when looking at the total absolute differences, the aggregation using the Equal weight decision maker based on distribution was better than most of the polls’ forecasts.

This thesis examines statistical methods to find the right timing of intrauterine insemination treatment relative to the start of the follow-up of the couples. Intrauterine insemination is a fertility treatment conducted by injecting refined sperm into a woman's uterus. Lots of research has been done on timing of steps within one IUI cycle. However, not a lot of research has been done on investigating if couples should be advised to start with the IUI immediately after consulting a fertility clinic, or wait a few more months to see if the pregnancy occurs naturally during this time. To analyze this problem, treatment strategies are defined in the following way: a couple stays on expectant management until some predetermined time when the first IUI cycle is started, unless they become pregnant before that time. Strategies analyzed involve starting the treatment at 0, 3, 6 or 9 months, or not at all until the end of the analysis, which is 1.5 years after diagnosis. Pregnancy probability for each couple is estimated with a multi-state Cox proportional hazards model. Then, the model is connected to the causal inference setting in order to compute the counterfactual pregnancy probability of each couple in the population. This thesis explores how multi-state models can be used to answer causal questions. To do this, a 3-state multi-state model is carefully connected to the causal inference theory and the assumptions this framework relies on are listed and commented upon. Treatment strategies are implemented through making an intervention on the IUI starting time. Then, a causal inference method, G-computation, is used to estimate the expected pregnancy probability of all couples in the population, given that everyone follows the same treatment strategy. Then, individual pregnancy probabilities are averaged in order to obtain the expected pregnancy rates in the population for each strategy. Methodology combining multi-state models and causal inference is new and only one similar study has been found so far in the literature. Multi-state models are currently used mostly for predictive analyses and it is of great interest to use them to answer causal questions as well. The results of this study show that there is no significant effect of the time the IUI has been started on the pregnancy rate in the population after 1.5 years, but there is significant difference between being and not being treated.

This thesis concerns itself with the effect of the normality assumption, the effects of discretisation choices and other assumptions made by software on prediction performance, when using Gaussian Bayesian Networks. To test these effects, different types of Bayesian Networks are constructed and made to perform predictions, using the same dataset. The dataset used contains records regarding the citations and other bibliometric statistics of articles published by authors aliated with the Delft University of Technology between 2010 and 2014. The first model is a Gaussian Bayesian Network (GBN), which assumes that the conditional probability distributions (CPD) of all variables concerned are Gaussian. The second model is a Multinomial Bayesian Network (MBN), which uses discrete variables. To accommodate to this model, the data is discretized. The third model is the Hybrid Bayesian Network (HBN, which can handle both discrete and continuous data and has no normality assumption on the distribution of the variables. The last model is a non-parametric Bayesian Network (NPBN). To compare the different models, they are used to perform a set of predictions in the form of quantile estimation. The results show that the GBN performs as well as the NPBN, when looking at the bulk of the data. When looking at data, where the mean citation score (mcs), the predicted variable, exceeds the 75-% quantile, the performance of the GBN becomes much worse than that of the NPBN.

Like other cities in Kathmandu Valley, Bhaktapur faces rapid urbanisation and population growth. Unsafe, new settlements are partly located at the floodplains and the government lags behind in implementing proper land-use policy to control unrestrained settlement. The rivers are not only constrained by uncontrolled settlements, but also by insufficient width and freeboard of bridges, and waste blockages causes problems. Combined with more extreme rain events during the monsoon due to climate change, flooding has become a reoccurring problem in Bhaktapur. To gain better understanding of the river and the corresponding flood risk, historical data is essential. Unfortunately, historical databases of water levels are non-existent for this river. Only starting from monsoon 2019, water levels and discharge have been measured on a regular basis. To reconstruct the missing historical data for a return level analysis, this research introduces the Classical Model for Structured Expert Judgment (SEJ) in combination with citizen science (CS). The objective of this research was to use Structured Expert Judgment in a flood risk analysis for the city of Bhaktapur. As a result of using SEJ, we were able to obtain sufficient water level data and estimate the return levels of extreme water levels of Hanumante river by fitting a Generalized Extreme Value distribution (GEV). This eventually led to a reverse Weibull fit, which in this case does not seem accurate. This research discusses in detail the advantages and issues of using Structured Expert Judgement in situations like this and also discusses the reliability of the results.

In this thesis, attention is paid to building different Bayesian networks. You can think of aspects such as parameter learning, search procedures and score functions. In addition, a distinction is made between the use of Discrete Bayesian Networks and Gaussian Networks. These models both have different assumptions which are also discussed. Finally, the theory is applied to publication and citation data for a group of Canadian researchers. We will build Bayesian networks with different techniques and try to predict and compare the performance of researchers. We will also build an algorithm based on clustering that can perform predictions by using one of the possible learning algorithms.

In this thesis Bayesian Networks are used to predict European football matches between the years 2008 and 2016. The goal of this research is to see how the structures learned by different Bayesian Network learning algorithms influences the predictions. First the data is explored and modified to be used for Bayesian Networks and secondly the theory is explained using examples. Finally the theory is applied on the data and the structures are learned with the help of a bootstrap method and the predictions are validated using 5-fold cross validation. We can conclude that the networks learned by the algorithms and with the help of an expert give a good representation of the underlying relationships, but are not very good in prediction the end result.

As an alternative energy carrier alongside electricity, hydrogen is considered one of the key factors in the impending required changes in the energy system transition. Due to the decrease in natural gas extraction in the Netherlands, the reuse of the natural gas network which eventually will become available for hydrogen transmission has emerged as a topic, recently. Although it seems to be possible to reuse the existing natural gas transmission network for the transmission of hydrogen, a quantitative risk analysis is still lacking and there is uncertainty about the safety of hydrogen transmission. This report aims to quantify the risk of the reuse of an existing natural gas pipeline for 100% hydrogen transmission and compare it with the natural gas case. A risk analysis entails the quantification of both the probability of failure and the adverse consequences. This research investigated the current methodology to determine the probability of failure for hydrogen transmission and proposed a new calculation method using a Bayesian network and historical natural gas data to derive new failure frequencies. The consequence of failure for both hydrogen and natural gas will be modelled using the SAFETI-NL; the influence of the gas different characteristics on the lethality will be quantified and risk values are produced, assuming the probability of failure to be similar for both gases when transported through natural gas pipelines. This research illustrated the promising application of a Bayesian network is a promising method to derive failure frequencies while taking into the significant influence of the pipeline characteristics. However, from the results, it emerges that further research is required with more redundant data. Also, future research should investigate the application of natural gas data since some failure scenarios are not entirely independent of the transmission gas, which could result in less favourable failure frequencies. Furthermore, calculations in SAFETI-NL have shown that hydrogen release is associated with a shorter duration and lower release power than natural gas, resulting in less significant consequences in the vicinity of the pipelines. Also, the low weight and high diffusive coefficient of hydrogen cause the consequences to decrease much faster with distance. As a result, there is concluded that hydrogen transmission is accompanied by lower risk values than natural gas, assuming the failure frequencies to be similar when both gases transported through natural gas pipelines. Although, numerous input parameters affect the risk values determined, of which at least the probability of ignition for hydrogen release has to be investigated in future research.