Recent advancements in causal inference and machine learning research have brought forward methods to estimate effects of interventions from observational data. The augmented inverse probability weighted (AIPW) estimator is such a method, which can be used to obtain estimates of potential outcomes. Potential outcomes are defined as a hypothetical outcome pair {Y(1),Y(0)}, of which only one outcome is observed in the data. Estimation of intervention effects boils down to effectively estimating these potential outcomes. Using the AIPW estimator, we aim to evaluate the average effect of increasing the energy efficiency of houses in the Netherlands on their expected transaction price. Moreover, we investigate how this expected effect changes when we condition on a certain subset of the data. Given that our assumptions hold, we find that on average, the estimated expected increase in transaction price is positive when improving the energy efficiency of a house. Improving an energy inefficient house to moderately energy efficient is expected to increase the transaction price by approximately €97.70,- per m2, while the improvement from moderately energy efficient to energy efficient increases the expected transaction price by approximately €20.96 per m2.  In general, older, smaller and more energy inefficient houses increase most in expected transaction price per m2 when their energy efficiency is improved.

Money laundering is an increasing problem for the global economy. To combat money laundering, banks use transaction monitoring models with particular thresholds to detect unusual transaction behaviour. However, it is a challenge to determine and evaluate the suitability of a threshold level to ensure that the risk of misclassification of transactions falls within the bank’s risk appetite. In the threshold tuning process, the suitability of a threshold level can be evaluated with a sample of the transactions below or above a threshold level which are reviewed by an analyst. One problem is that the review process of transactions during the threshold tuning process is timeconsuming. In addition, banks want to be able to quantify the risk of misclassification of transactions to determine whether this falls within their risk appetite. This underlines the need to develop a threshold tuning strategy to accelerate the threshold tuning process in which the risk of misclassification of transactions can be quantified to determine whether it falls within the bank’s risk appetite. To accelerate the threshold tuning process, a framework was developed and five threshold tuning strategies were established which evaluate the suitability of different threshold levels with a given strategy. In addition, several methods to determine a confidence interval were examined to quantify the risk of misclassification and to ensure that it falls within the bank’s risk appetite. The threshold tuning strategies were compared and evaluated on the required amount of reviews of transactions and the difference between the found and true threshold level using synthetic data sets. Overall, the bisection threshold tuning strategy is recommended, since this strategy resulted in the lowest number of required reviews of transactions and resulted in a small difference between the found and true threshold level. The results of the synthetic data sets were promising, but more experiments with preferably real transaction data or other distributions are required to further evolve and fully validate the framework and proposed bisection strategy. The work presented in this thesis contributed to a more risk-based approach to enhance the efficiency and effectiveness of the threshold tuning process of transaction monitoring models.

The field of deep reinforcement learning has seen major successes recently, achieving superhuman performance in discrete games such as Go and the Atari domain, as well as astounding results in continuous robot locomotion tasks. However, the correct specification of human intentions in a reward function is highly challenging, which is why state-of-the-art methods lack interpretability and may lead to unforeseen societal impacts when deployed in the real world. To tackle this, we propose multi-objective reinforced active learning (MORAL), a novel framework based on inverse reinforcement learning for combining a diverse set of human norms into a single Pareto optimal policy. We show that through the combination of active preference learning and multi-objective decision-making, one can interactively train an agent to trade off a variety of learned norms as well as primary reward functions, thus mitigating negative side effects. Furthermore, we introduce two toy environments called Burning Warehouse and Delivery, which allow for studying the scalability of our approach in both size of the state space and reward complexity. We find that through mixing expert demonstrations and preferences, we can achieve superior efficiency compared to employing a single type of expert feedback and, finally, suggest that unlike previous literature, MORAL is able to learn a deep reward model consisting of multiple expert utility functions.

This thesis aims to develop a methodology for predicting the swap spread, which is defined as the difference between the German government bond interest rate and the Euribor swap rate. Thus far, the prediction of interest rates is limited to the prediction of a single interest rate. This thesis introduces the simultaneous prediction of the spread between two correlated interest rate curves. The methodology developed in this thesis considers the dependence between the bond rate and the swap rate. The study utilizes a Dynamic Nelson-Siegel (DNS) model, which is extended to incorporate the correlation between these two rates. The simulation studies reveal that the variants simultaneously predicting both the swap and bond rates using a restricted VAR(1) model for factor dynamics outperform the other variants in predicting the swap spread. Another important aspect considered is the stationarity of the latent factors. The simulation studies demonstrate that the stationarity of the empirical DNS factors accurately represents the stationarity of the true DNS factors. This motivates the reformulation of the DNS model into a new variant where the first-order differences of both the swap and bond rate latent factors are modeled by a restricted VAR(1) model. A case study validates the developed new variant of the DNS model, demonstrating predictions for the swap and bond curves that have an accuracy comparable to the accuracy of the benchmark model. The key advantage of the DNS model over this benchmark model is that the DNS model predicts the swap curve and bond curve over the whole maturity spectrum. The prediction over the whole maturity spectrum is crucial to compute the spread between the two rates, which emphasizes the relevance of the new model presented in this thesis.

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.

This thesis showcases a rather contemporary method of solving a generalized system of stochastic differential equations (SDE's) comparable to the SABR model. The solution is derived from a stochastic-local volatility (SLV) model in which the local volatility (LV) component is kept general. This generality is maintained throughout all derivations, eventually yielding a model containing an undefined LV function. This function can then be specified however the user of the model deems suitable, as long as minor constraints are satisfied. Obviously, this is a very valuable quality of the model as it is highly customizable. The solution consists of a set of pricing functions that seemingly possess all the aforementioned desirable properties, i.e. fast in evaluation, computational tractability, flexibility etc., with little disadvantages. The generalized SLV model that is used is typically denoted in the form of two SDE's, though in the majority of this thesis an atypical three SDE form is used. This extended system is used to isolate the LV component, in turn enabling for appropriate application of an SDE transformation called the Lamperti transform, which will provide the key to solving the entire system. The Lamperti transform is a highly versatile method for transforming SDE's into new equations typically more suitable for simulation and parameter estimation procedures, and its inner-workings and various applications will be the main focus of this thesis.

This thesis evaluates the pass-through of the 2001 and 2012 Dutch Value Added Tax (VAT) increases to customer prices using a difference-in-differences model. To this end, the first difference and feasible generalised least squares estimators are introduced. Contrary to the conventional pooled OLS estimator, these estimators always show significant causal effects for both VAT hikes. These also dramatically improve the accuracy of the estimates compared to earlier research on the incidence of VAT. For the 2012 tax increase, the null hypothesis of full pass through is even rejected. This result is a novelty in the econometric literature. Even in more general settings, the estimators used in this thesis prove far superior over conventional causal estimation techniques of difference-in-differences models.

In this thesis, sensitivity analysis is used to study the influences of parameters on specific outputs in the hydrodynamic model 3D DCSM-FM of the North Sea. The sensitivity analysis is the study of how uncertainty in the outputs of a model can be divided and allocated to different sources of uncertainty in its inputs. The software Delft3D FM is used to simulate the model, which is developed by Deltares. This thesis is supported by German pilot of the UNITED project, which studies the possibilities of combing blue mussel and sugar kelp cultivation with wind energy. The investigation is conducted at FINO3 platform, 80 km off Sylt. In this thesis project, temperature and current velocity are selected as outputs in sensitivity analysis, which are influential factors of blue mussel and sugar kelp growth. Specific parameters in the hydrodynamic model are selected as inputs respectively. Three sensitivity methods are conducted: Morris, copula-based and variance-based method. Among them, copula-based and variance-based consider the independency information, while parameters are assumed dependent in Morris method. To generate samples, parameters are transformed into a unit hypercube in Morris method and run on the contour of the grid cell, composing paths. Between two steps within the paths, only one parameter changes at a time (OAT method). The input domain is scanned with a better strategy to separate the paths maximizing the dispersion. Each parameter’s elementary effects are calculated within paths, evaluating the changes in outputs contributed by the single parameter. Then (absolute) mean and variance of elementary effects are used as sensitivity indices. Copula-based method uses similar sampling and the same measurements, but it gathers parameters into copulas before sampling to include the dependency information. In variance-based method, the variance of the outputs’ conditional expectations is used to measure the sensitivity. Only random samples are needed in this method. Morris and copula-based method prove the temporal and spatial similarities of parameters’ sensitivity behavior. Convective and evaporative heat flux are the most influential parameters of temperature, and they also show correlations with other parameters. Air density influences current velocity the most, while Smagorinsky factor is the most correlated parameter of current velocity. Variance-based method gives similar results about rankings of influences. Correlations are proved to exist among parameters. Uniform horizontal eddy viscosity/viscosity in definition files have no impacts, as they are overwritten. Three methods are compared. Except the differences in independency, sampling and measurement, there are some other differences. Much more samples are required in variance-based method and it is used mainly to decide the existence of significant correlations and whether a parameter can be neglected. While Morris and copula-based method ranks the influences and correlations.

This thesis gathers, develops and evaluates several characterizations of multivariate tail dependence. It is established that the stable tail dependence function (STDF) is a suitable copula-based dependence function that fully captures the multivariate extremal dependence structure in all dimensions d≥2 and can be used to visualize the tail dependence structure for bivariate and trivariate problems. Based on the STDF, we propose a multivariate tail dependence coefficient (TDC) as an extension of the well-known bivariate TDC. Importantly, we show that the proposed measure can identify tail independence in all dimensions d≥2, similar to its bivariate variant. The performance of nonparametric estimators for the STDF and, inherently, the multivariate TDC, is assessed with an extensive simulation study, including smoothed and bias-corrected versions of the empirical STDF. Based on the estimators for the STDF and the multivariate TDC, test statistics under the null hypothesis of tail independence are developed and evaluated in another simulation study. The STDF-based estimation and testing procedures are applied to foreign exchange (FX) data to characterize the tail dependence structure between three European FX rates and five worldwide FX rates.

The Morris method is a widely used screening method in sensitivity analysis. The method assumes that the input parameters are independent of each other. To overcome the assumption a copula-based Morris method is proposed. In this report the results of taking the dependencies into account are analyzed for the Morris method. For two examples sensitivity analysis is performed with the Morris method, with copula-based Morris method and by calculating sample correlations with a Monte Carlo simulation. From the analysis it follows that taking dependencies into account can have varying effects for different methods. It turns out that a straight-forward implementation makes the method often practically unusable. The sampling of model evaluation points becomes too computer expensive. The amount of copula evaluations is growing exponentially with the dimension and for copulas without an analytic expression these are already lengthy. The computational intensity can be reduced in two ways. First, one can approximate the probabilities. Different ways of approximating the probabilities are researched. Numerically integrating with the midpoint rule seems to be the best way of approximating the probabilities in the copula-based Morris method. Next to approximating the probabilities, one can also use the independent groups when implementing the method. When the input parameters are correlated there are usually a few groups of correlated parameters rather than that all the parameters are correlated with each other. This can be utilized to more efficiently implement the copula-based Morris method. When the group sizes are not increasing the computational intensity depends linearly instead of exponentially on the number of model parameters. By using both improvements the method can generally be applied to tens or hundreds of parameters in reasonable time, which is desired for a screening method.

This bachelor thesis is about binary error-correcting codes. A binary code is a collection words with the same length n that consists only of zeroes and ones. The error-correcting quality of a code is determined by the Hamming distance d of a code. A classical question in coding theory is: What is the maximum number of codewords in a code with length n and Hamming distance d? This maximum is denoted with A(n,d). Determining A(n,d) is quite difficult and often we have to make due with lower and upper bounds on A(n,d). In this thesis we compare six different bounds for finding an upper bound on A(n,d), give a detailed description of each bound, a proof and a clarifying example. The main focus of this thesis lies on the linear programming bound (with extra constraints). For d=4 we dive deeper into the linear programming bound and the Krawtchouck polynomials it uses. Finally we draw some conclusions from the comparisons of the different types of bounds.

Building models for an electric vehicles usage data set in order to simulate virtual populations of these electric vehicle users. With these simulated populations charging strategies for electric vehicle users could be developed in order to improve the use of electric vehicles. The modeling is done with copula functions, and are compared with different tests.

Prisons serve as amplifiers of Tuberculosis (TB) transmission due to overpopulation, lack of hygiene, and bad ventilation [Mabud et al., 2019] [Baussano et al., 2010]. The risk of TB is elevated during and after incarceration, only returning to the general population’s risk seven years after liberation. This is an indication that formerly-incarcerated individuals are a highrisk group. By preventing TB among ex-prisoners, the burden and transmission to the general population can remain limited. This study aims to analyze the cost-effectiveness of various preventive measures among formerly-incarcerated individuals in Brazil. With the imprisonment rate growing in the country and the high TB incidence rates, Brazil can benefit greatly from proposed measures. The research mathematically models the effect of several interventions and quantifies associated health benefits and costs with the use of Disability Adjusted Life Years and Incremental Cost-Effectiveness Ratios. The parameters of the model are estimated with Bayesian statistics, using likelihood functions and prior distributions to calculate a posterior distribution. The results of the research indicate how the different interventions behave and which is most advisable for implementation in the Brazilian health system. Our conclusion is that shorter preventive therapies in combination with the skin test Tuberculin Skin Test perform better than longer therapies and/or the blood test Interferon Gamma Release Assays. This research was conducted in collaboration with the Harvard T.H. Chan School of Public Health and the TU Delft, with help from the Brazilian ministry of health.

In this thesis, we present a study to obtain a clear and accurate overview of the progress and behaviour of COVID-19 in the Netherlands. We distinguish two parts for this study. The first part is to estimate the total number of infected people as a function of time by combining data from hospital admissions, daily reported cases and serological data. Using these data sets, we found that our estimation for the number of infected people was comparable to the estimations provided by the RIVM and Sanquin. Furthermore, we found that on average only 39.3% of the total number of cases were detected. 1.2% of the total number of infected people is admitted to the hospital and 18.6% of the hospitalized patients is admitted to the ICU. The second part is to develop a representative model that reproduces the estimated total number of infections using a modified SEIR model. These modifications include modelling the infection rate β(t) as a function of time using a simple linear ODE, a system of ODEs inspired by the Lotka-Volterra equations, the implementation of gamma distributed exposed and infected stages and lastly the incorporation of spatial heterogeneity. We found that our Lotka-Volterra inspired model was able to model multiple consecutive waves, which differs from the standard compartmental models. The other modifications however seemed to have only minor effects on the model and had some difficulties with matching historical data. We conclude that our Lotka-Volterra inspired model should be used to model consecutive waves for a longer period of time. The other modifications can be used to optimize the model.

In this modern age, data is being generated constantly and data is being saved for analysis everywhere. In the maritime industry, interest in the analysis of ship data has grown over the years. In this thesis, we will take a look at AIS data coupled with sea state data. AIS data is data generated from the ship, concerning the ship locations, speed, and heading, among others. When coupled with data such as the wave height and wave directions at these locations, we can analyse the ship operations in different sea conditions. We analyzed 46 Damen ships of the same type, that operate in different regions of the world. The aim was to make interpretable groups of ships that have similar operation profiles, and to investigate the effect of different sea states on the ship operations. We first enrich the data with port labels, from which we can define trips as sequences of points away from port. We also estimate path lengths between points using Bézier curves. From this we get a relevant set of variables that can use for an unsupervised learning task. We clustered the ships using three methods: principal components analysis, Kmeans, and hierarchical clustering. Principal components analysis showed variation in the ships, but interpretation and definitive clusters were not clear. We then used the K-means method to make 12 clusters of ships, of which six clusters proved to be stable. Hierarchical clustering showed similar results. Interpretation of these clusters was possible, mainly by looking at separate trips. We therefore also clustered the trips, to get classes of trips. We used the K-means method and obtained six clusters of trips, of which five were stable. We also look at ship availability in different regions during different sea conditions. We use an isotonic regression method to test whether ships ships stay in port more often during heavy weather. We found regions where availability decreases during high waves and regions where availability seemed independent from wave height. This most likely has to do with the function of the ship. And finally we look at sailing speeds during different sea states and find that sea state data alone is not sufficient to adequately estimate sailing speeds of a ship. The conclusion is that using the variables that we created, stable clusters can be obtained. These clusters are interpretable and can lead to a better understanding of customer needs. Coupling the AIS data with more data sources however would be a recommendation, since that can lead to more informative clusters, and might lead to more insight into sailing speeds.

Trace metals appear in estuarine systems in two forms: dissolved and particulate. Describing the partitioning between these two forms is done by a coefficient, K_d, which relies on a number of environmental parameters, such as the salinity of the water and the seasonally dependent biological activity. Although this coefficient is known to follow a log-normal distribution, models describing estuarine metal dynamics usually simply use average values. In this study an attempt has been made to create a statistical model of K_d in the Scheldt estuary for a number of trace metals, based on data of some environmental parameters. This model should be able to cover the whole spectrum of K_d values. The used parameters are salinity, the suspended particulate matter concentration, the total metal concentration and the year of measurement. A comparison is made between two linear regression based models, principal components regression and partial least squares regression, and two decision tree based models, random forest and gradient boosting machine. Although cross-validation performance on the training set is promising, with the decision tree based models clearly outperforming the linear regression based ones, predictions on an independent test set are very poor for all metals except for cadmium. Cadmium is an exception, because its estuarine dynamics are mainly governed by a specific process, that is driven by changes in salinity. The dynamics of all other metals depend on both the biochemical and the physical characteristics of the estuary. In the proposed model the parameter 'salinity' has to account for both of these characteristics simultaneously, which is inherently impossible. Inclusion of pH and or dissolved oxygen content seems promising to create an adequate model. The first, because it is correlated to salinity, and the second because it is representative for the seasonal variation.

Banks are financial institutions that lend money from other parties and provide loans to individuals and organisation for a higher interest. Lending out money is associated with the risk that debtors are not able to fully or partially repay the loans. This is called credit risk. Banks have to make an estimate of the credit risk in their portfolios and have to keep reserves for potential losses. The way this risk is to be determined, is decided by the government where the bank is established. In Europe, the United States, Russia, China among others, the legislation on credit risk is derived from Basel III. Basel III is an international framework to homogenise banking regulation across the world. There are three important factors to determine credit risk In Basel III, namely Probability of Default, Loss Given Default and Exposure at Default. In this thesis I investigate Probability of Default (PD) modelling. The size of the portfolio, for which the Probability of Default has to be estimated, can vary greatly. When the amount of defaults in a portfolio is low and the amount of explanatory variables is high, there is a risk of overfitting. Variable selection methods can be used to counteract overfitting and give understanding of the important predictors. I apply variable selection methods on on a logistic regression. I look at three Frequentist variable selection methods, namely Forward Selection, Lasso and Relaxed Lasso. I compare these three methods with Predictive Projection combined with a Horseshoe prior, which is a Bayesian approach to variable selection. Forward Selection starts with only the intercept in the model and adds variables one by one to the model. The variables are added in such a way that each step increase the estimated performance the most. The Horseshoe prior and Lasso Regression are types of regularisation, where the estimates of the regression coefficients of the logistic regression get shrunk to zero. In Lasso regression, this is done by adding a L1 penalty of the regression coefficients to the logistic regression. This causes weak signals to be pulled to zero. Lasso shrinks all regression coefficients to zero to some degree, even those with a strong signal. Lasso can also be used to and an order of importance for the regression coefficients by varying the strength of the L1 penalty. Regression coefficients are set to zero one-by-one as the penalty increases. Relaxed Lasso uses this rank and refits the variables without regularisation. In Bayesian statics, regularisation is added via the prior. The Horseshoe prior can adjust to the average sparsity in the model and the Horseshoe prior either shrinks a signal aggressively to zero, or leaves the signal almost unchanged. The posterior of the model is never truly sparse. Predictive Projection can induce sparsity by setting the Monte Carlo samples of the posterior to zero for certain variables. This is done in such a way that the Kullback-Leibler divergence between the full posterior and the projected sparser posterior is minimised. I investigate the behaviour of the variable selection methods. The main focus is on the predictive performance, the sparsity, the computation time and the reliability of the estimated performance for the selected models. I apply the methods to various types of simulated data to compare the variable selection methods. The simulated data consist of data with independent predictors, collinear predictors and non-normal predictors, among others. The simulations studies show that Lasso and Predictive Projection lead to models with the highest performance overall and the predictive performance is more stable over different realisation of the data. For the same performance the Predictive Projection produces models with less variables. This makes Predictive Projection the most attractive method. I also employ the techniques to FreddieMac data, which is a data set on single-family mortgages. The results are similar to the simulated data and Predictive Projection with the Horseshoe prior is the most attractive variable selection method. Both the simulation studies and the FreddieMac application imply that the estimated performance of the Predictive Projection and Lasso are better than those of Forward Selection and Relaxed Lasso. However, the behaviour of the estimated performance remain unclear to a certain degree. More simulations per data type and more data types are needed for more insight into the estimated performance. Additional resources are needed to achieve this.

Safe hypothesis tests are tests that are robust under accumulation bias, namely when there are dependencies between the results of previous studies and the decision whether to conduct further studies. We construct two types of safe test for the 2 × 2 contingency table, the conditional and unconditional safe tests. In general safe tests are given by an information projection that may be difficult to compute. The conditional tests we construct however are given either in explicit form or implicitly via a defining equation. The same can be said of many of the unconditional tests we construct, for which we prove a number of theoretical results enabling their quick calculation when not given explicitly. The method we develop to accomplish this may perhaps be used to identify optimal safe tests in many other scenarios.