This study focuses on optimizing the efficiency of single-lane roundabouts for connected automated vehicles (CAVs). While roundabouts are vital for traffic management, their performance declines significantly under high traffic volumes. By leveraging vehicle-to-vehicle communication and the cooperative decision-making capabilities of CAVs, this research develops a microscopic control model that not only minimizes sojourn times (maximizes efficiency) but also provides precise trajectory control for each individual vehicle. Besides, a theoretical M/G/1/k queueing model is employed to calculate the expected sojourn time, serving as a baseline to compare CAV-controlled scenarios with human-driven conditions. The results demonstrate that the proposed microscopic control model significantly reduces the expected sojourn time for vehicles entering the roundabout. For a single-lane roundabout with a capacity of 17 vehicles per leg, compared to uncontrolled scenarios simulated in VISSIM, the control model achieves empirical efficiency improvements of 26%, 80%, 91%, and 90% under arrival rates of 200, 400, 600, and 800pcu/h per leg, respectively. These empirical findings align closely with theoretical predictions from the M/G/1/k queueing model, which estimate efficiency gains of 18%, 78%, 89%, and 90%. Moreover, the control model demonstrates robustness under extreme traffic conditions, maintaining high efficiency and passenger comfort. This research provides valuable insights into the integration of CAVs into traffic systems and contributes both practically and theoretically to the modernization of roundabout traffic management.

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.

As machine learning algorithms become increasingly complex, the need for transparent and interpretable models grows more critical. Shapley values, a local explanation method derived from cooperative game theory, is an explanatory method that describes the feature attribution of machine learning models. This is defined by the contribution a feature has to one single prediction. In this thesis the Shapley value formula is detailed, along with its properties. Three different ways to approximate the Shapley values are then introduced: Monte Carlo method for value function, Monte Carlo method through permutations and Kernel SHAP. Implementation of these methods using different datasets reveals that while both methods produce nearly identical Shapley values, Kernel SHAP is significantly faster. This research contributes to the field by demonstrating the advantages of integrating Shapley values into machine learning models, to enhance model transparency and trustworthiness.

The widespread use of Markov Chain Monte Carlo (MCMC) methods for high-dimensional applications has motivated research into the scalability of these algorithms with respect to the dimension of the problem. Despite this, numerous problems concerning output analysis in high-dimensional settings have remained unaddressed. We present novel quantitative Gaussian approximation results for a broad range of MCMC algorithms. Notably, we analyse the dependency of the obtained approximation errors on the dimension of both the target distribution and the feature space. We demonstrate how these Gaussian approximations can be applied in output analysis. This includes determining the simulation effort required to guarantee Markov chain central limit theorems and consistent estimation of the variance and effective sample size in high-dimensional settings. We give quantitative convergence bounds for termination criteria and show that the termination time of a wide class of MCMC algorithms scales polynomially in dimension while ensuring a desired level of precision. Our results offer guidance to practitioners for obtaining appropriate standard errors and deciding the minimum simulation effort of MCMC algorithms in both multivariate and high-dimensional settings@en

Technological progress irreversibly changes the nature of sports. The relevance of technology in sports can be seen with relative ease to most spectators in tennis, football and many other elite sports. Some technologies have changed the sport in a way that many spectators might not be aware of. Behind any professional sport, there are countless hours of training and preparation. Athletes are pushing their own limits in achieving perfection. Coaches are trying to make sure that the training the athletes go through results in improvement of their performance, but without straining themselves too much which can lead to an injury. The technology of today helps with this training process and coaches need to be able to use it to provide good feedback to their athletes.
This thesis is written in the context of the Citius Altius Sanius (CAS) project aimed at injury prevention and performance improvement in sports. The CAS project combines the expertise of data scientists, industrial designers and biomechanical engineers together with the resources of sports associations and sports equipment designers among others. The goal of the CAS project is to initiate collaboration between various universities and departments to develop sensor technology, provide analysis based on the sensor data and provide a clear guideline of feedback to the athlete.
The primary goal of this thesis is to extract meaningful insights from sensor data through statistical modeling. Two sources of sensor data are used within the thesis: data from prototype sensor trousers worn by football players during training and data from a sensor sleeve worn by tennis players during serve practice. The research employs supervised learning algorithms within the framework of machine learning and deep learning models for capturing intricate patterns in the data as well as functional data analysis techniques such as functional principal components analysis and functional regression models applied for imputation purposes and dimension reduction.
We used neural network architecture, which mixes both convolutional and recurrent layers, consistently throughout this thesis. The main application of this network lies in recognizing football-related activities using sensor data. The neural network achieves good accuracy and is easily adaptable to other human activity recognition problems. We also considered various other models for this task, however none could match the computational speed and accuracy of the neural network. Nonetheless, given a plethora of methods that were tested and dissatisfaction with the accuracy measures used to assess the goodness-of-fit of the tested methods, a novel quality measure was introduced for activity recognition problems, to leverage the domain knowledge for the purpose of determining accuracy of an activity recognition method. In the case of our application, one of the constraints is the length of activities that are predicted. This measure accounts for the fact that activities such as jumping or passing a ball realistically have a minimum duration. Instances where a prediction model outputs an activity shorter than physically plausible incur harsh penalties.
We also propose a novel post-processing procedure tailored specifically to human activity recognition problems, ensuring that predictive models adhere to physical constraints, such as the minimum duration of activities. This post-processing method aims to increase the accuracy of prediction models which violate these constraints and as a result, to narrow the gap in accuracy between different prediction methods.
In the context of tennis, we encountered difficulties in predicting the serve performance metrics using sensor data. While predicting the ball speed can be easily achieved, accurately predicting the velocity-accuracy index (VA index), which combines ball speed with serve accuracy, proved more complex. To assess the effectiveness of our model in distinguishing true predictions from noise, we applied a permutation test. Notably, the main contribution of this research lies in the rigorous formulation of the null hypothesis for this test, linking it to established permutation test theory.
This research contributes to the fields of sports science and data analysis by offering insights into activity recognition and performance prediction using sensor data. The methodologies developed here have potential applications across various other sports as well as activities unrelated to sports. While data provided for purposes of this research comes from wearable sensors, it is possible to also apply these models and procedures in other types of sensor data or even beyond.@en

Through the expansion of large-scale service systems and the exponential growth of data generated by complex IT infrastructure components, gaining a comprehensive overview of the different levels of service within an IT system has become increasingly challenging. In particular, this brought to the fore the question from a large commercial bank of how IT monitoring data streams generated by their complex IT infrastructure can be associated with one another.

In more detail, the data from the monitoring stream consists (among other things) of a message and a time stamp. Moreover, the monitoring data stream of this bank consists of two natures of information. These natures are either automatically generated warnings in the form of events or unplanned outages, referred to as incidents. The events and incidents are referred to as arrivals. As a first requirement to obtain better granularity, both event and incident messages with similar semantics should be grouped together. To this extent, the message component from each arrival is transformed into a numerical vector, the dimension of the obtained vector is reduced, and the collection of vectors is clustered. Once the individual arrival from the IT monitoring data stream is attached to a cluster based on their message component, the arrival is assigned a mark. This mark consists of a combination of the assigned cluster, the nature, and three different levels of service from the IT architecture on which the arrival occurred.

From a mathematical point of view, we can now view the monitoring data stream from different levels of service as a marked point process. Our primary focus centers on a specific category of marked point processes, known as marked Hawkes processes. Given the marked Hawkes process, we assume that each arrival from the IT monitoring data stream results in an instantaneous increase in the probability of some other arrivals in the near future. From here, we estimate the excitation matrix, representing the instantaneous increases among all assigned marks. Once the estimated excitation matrix is obtained, we decompose it into the different levels of service as defined within the mark. In particular, the decomposition has been performed through means of hierarchical linear models. Finally, the decomposition resulted in a comprehensive overview of the excitation behavior in large-scale service systems. This overview can directly be incorporated into the field of Software Architecture in order to uncover associations within complex IT infrastructures.

With the rise of zero-shot synthetic image generation models, such as Stability.ai's Stable Diffusion, OpenAI's DALLE or Google's Imagen, the need for powerful tools to detect synthetic generated images has never been higher. In this thesis we contribute to this goal by considering wavelet-based approaches for synthetic image detection.

We will introduce multi-level discrete wavelet transform, which to the best of our knowledge has never been considered for this goal prior to this work. A similar approach that has been considered for the goal of synthetic image detection, is the multi-level wavelet packet transform used by Wolter et al. We will show that not only is our proposed approach more efficient and easier interpretable, it also performs better in a number of experimental settings and therefore forms a suitable addition to the toolset for the detection of synthetic images.

Moreover, we will try and generalize performance of our used classifiers to out-of-dataset samples and see that our used classifier in general does not allow for such generalization. Finally, we will discuss the challenges of this work and offer interesting directions for further research.

Pancreatic ductal adenocarcinoma (PDAC) is a devastating disease with a high mortality rate, poor prognosis, and a mere 7.7% 5-year survival rate [1] compared to 65% for all cancer types [2]. Approximately 80% of patients are diagnosed at the advanced stage [3], for which only palliative chemo(radio)therapy remains as treatment option. However, the efficacy of chemotherapy varies among patients, e.g. FOLFIRINOX has a response rate of only 25-30% in metastatic patients and a disease control rate of 70.95% [4]. Therefore, stratifying patients is crucial for individual benefit and for addressing the socioeconomic challenge of rising healthcare costs and increasing cancer incidence. This master thesis aims to investigate the relationships between tumor markers CA19-9 and CEA as well as blood marker data, both before and after one cycle of FOLFIRINOX and their correlation to the chemotherapy response. The goal is to subsequently develop a robust classification model to improve patient stratification and facilitate personalized treatment approaches. The analyzed cohort comprises 247 PDAC patients of which 55% are male and 45% are female participants. Among them, 152 had (borderline) resectable, 54 locally advanced and 41 metastatic PDAC. All patients received FOLFIRINOX treatment, and tumor responses were categorized using RECIST 1.1 [5]. First a thorough data analysis, including outlier and principal component analysis (PCA) is conducted to identify patterns and relationships between and within variables. Subsequently, a robust classification model was built using random forest modeling, accounting for dataset imbalance. Three optimal models are proposed based on (a) only pre-chemotherapy values, (b) values before and after the first FOLFIRINOX cycle and (c) only the top 10 identified variables in (b). For each of the most important variables, partial dependence and accumulated local effect plots are generated to gain further insights into their marginal effect on the classification outcomes. The initial data analysis revealed the prognostic and predictive significance of the tumor marker CA19-9, both before and after one cycle of treatment, and the difference in its levels. Additionally, various blood markers, including Hemoglobin, Thrombocytes and γ-Glutamyl Transferase, showed associations with treatment outcomes. The assessment of variable importance further confirmed these relationships between tumor and blood markers and their impact on treatment response. However, PCA did not identify significant patterns or relationships within or between groups of blood markers. Moreover, the developed random forest classification models exhibited promising balanced accuracy, with values of 0.97, 0.98, and 0.90 for models (a), (b), and (c), respectively, in stratifying PDAC patients into the two distinct response groups (disease control and progressive disease), facilitating treatment decision-making. In conclusion, this master thesis emphasizes the crucial role of comprehensive and rigorous data analysis in PDAC research, particularly when employing machine learning for predicting treatment outcomes. Integrating information from measured tumor and blood markers into the random forest models enables the prediction to FOLFIRINOX therapy both before and after one cycle. The implications of these findings are significant, as they can lead to improved patient management, efficient allocation of resources, personalized approaches, and contribution to the research and development efforts in PDAC. To validate and expand upon the presented results, further studies are required, ultimately advancing the field of personalized medicine in pancreatic cancer. Keywords: pancreatic cancer, PDAC, prediction model, random forest, data analysis, outlier analysis, principal component analysis.

During the initial phase of diagnosis, patients with anti-NDMA-receptor encephalitis (anti-NMDARE) often experience severe symptoms that significantly impact their quality of life. Anti-NDMARE is an autoimmune disorder affecting the brain, with electroencephalography (EEG) playing a vital role in diagnosis and treatment. Identifying EEG patterns associated with positive or negative prognosis is crucial for adjusting treatment intensity. Improved understanding of diagnosis, prognosis and treatment could enhance the quality of life for anti-NDMARE patients. This thesis aimed to analyse the EEG data with Machine Learning (ML) to predict which patients exhibit positive recovery after 12 months of standard treatment.

To predict the outcome after 12 months, a Random Forest (RF) classifier was constructed using available EEG features. The EEG dataset exhibited a clustered structure due to multiple values for each patient’s EEG features. Three approaches were considered to handle this clustering: ignoring clustering, reducing clustering to independent observations, and explicitly accounting for clustering. The first two options were explored in this research. Another prominent challenge encountered early in the research was the class imbalance, which was addressed by under- and oversampling the dataset.

For the simulation sets, under- or oversampling did not yield the desired effect, as the normal sets demonstrated comparable or even superior performance compared to the the under- and oversampled sets. However, under- and oversampling improved the performance scores for the real dataset. Reducing the clusters to independent observations did not achieve high performance scores compared to ignoring clustering, both in the simulation and real data cases. Furthermore, in both cases, RF models using the EEG sets outperformed those using principal component analysis (PCA) on the clustered EEG set.

Although the performance metrics scores were not yet optimal, important features for determining class labels were identified, providing a good understanding of the dataset. Mean Decrease in Impurity (MDI) and SHAP algorithm highlighted the significance of connectivity-related features in the reduced clustering to independent observation setting. The relevance of these features became evident upon calculating the mean, minimum, or maximum. In the EEG setting, MDI emphasized the importance of the features deltapower, sampleentropy and occipital-related features. These features remain important in the reduced set. SHAP, in addition to prioritizing the same features, offered insights into how specific features contribute to the prediction of a specific observation, enhancing interpretability.

The challenges for the RF classifier in the case of anti-NDMARE are class imbalance and accurate classification of the minority class. Under- and oversampling techniques successfully improved classification of minority class observations for the original EEG set. Concluding, this set is strongly encouraged to be utilized over all sets when aiming to classify EEG features. However, this set overlooks the clustering aspect, leaving room for optimization in future research to address this limitation. Additionally, it is recommended to explore the potential of a Convolutional Neural Network (CNN) for accurate classification of raw EEG signals. Its exploration was beyond the scope of this research.

There is a raising demand for player statistics in the world of football. With the developments over the last years in wearable sensors, Human Activity Recognition (HAR) based on wearable IMU sensors can be used to tackle this problem. This thesis builds upon an earlier research done for this topic, where an end-to-end pipeline based on deep learning was created that is able to be trained and used for football activity recognition. The goal is to test and improve said pipeline. This was done by adding change of directions (COD’s) to the classifiable activities. Furthermore, run velocities were build as a spectrum with several categories depending on the speed. A combination of convolutional and recurrent layers resulted in test accuracies up to 88.9%.
Afterwards, the pipeline was used to evaluate larger datasets containing football drill and a football physiotherapy training. For this a sliding window evaluation procedure was proposed. These evaluations gave promising results. Many actions and football related activities could be recognized, however many smaller, shorter actions were missed. This can be seen as lack in trainingdata. In this data, little activities with the ball were present. Hence the deep learning models could not be trained accordingly. Later, it was researched
if additional training of activities with ball increased the evaluation. This was indeed confirmed, since the evaluations showed more detailed and realistic results. Including even more additional trainingdata, could result in the pipeline performing reliably in real-life football scenario’s.

This paper presents a novel approach for the estimation of conditional multivariate cumulative distribution functions (CDFs) within a nonparametric framework. To achieve this, we introduce a binary random variable that indirectly represents conditional CDFs and construct a dataset by pairing input vectors with the binary variables. We developed a general approach compatible with various machine learning methods.
We have also developed an R package that facilitates the application of machine learning methods. This package leverages a range of machine learning models, including decision trees, neural networks, random forests, and bagging neural networks. Through systematic learning of the intricate relationships between the covariates and the binary variables, we effectively estimate conditional CDFs.
To enhance the accuracy and reliability of the estimated CDFs, we incorporate a rearrangement technique which transforms the estimated functions into monotonic representations, aligning them more closely with the target CDFs and mitigating potential inconsistencies [6].
Through simulations, we evaluate the performance of the estimation approach under various scenarios and assess the impact of sample size and correlation on estimation accuracy, using Mean Integrated Squared Error as a key performance metric. The results demonstrate the effectiveness and robustness of the methodology in estimating conditional CDFs, providing a valuable tool for capturing complex dependencies in multivariate data, with potential applications in risk assessment, finance, and environmental modeling.

Even though the use case of this study was to predict water currents for the sailing regatta in Tokyo, the method can be used for many different applications.

Thanks to increasing computational resources, the grid sizes of global climate and weather prediction models are decreasing to scales at which subgrid processes, especially the evolution of clouds, can become spatially too variable for traditional deterministic parameterization approaches. We propose a stochastic parameterization in which clouds are represented by a Markov-Chain (MC) lattice model. The state of each lattice site is characterized by cloud top height (CTH) and cloud optical depth (COD). Based on these two parameters, clouds can be categorized into different cloud types (cumulus, stratus, cirrus, deep convection, etc.). In contrast to previous work, where the transition probabilities between different cloud types were calculated, we determine the transition probability densities in the continuous CTH-COD domain. We moreover explore the influence of neighbouring lattice sites on these transition densities to research whether it is possible to simulate cloud organization structures, without the use of extra external large scale variables or forcings. We estimate the parameters of the distributions using GOES-16 satellite images. Using these estimates, we perform simulations of the continuous state space Markov Chain over the lattice. This results in 2D spatial cloud evolutions, which spatial organization we compare to the original images.
The simulations did not show any spatial structures as were observed in the original images. All the simulations resulted in a granulated image of different cloud types after only a couple of hours.
A simulation from the MC model describing transitions from a finite number of cloud types converges to the observed occurrence frequencies, which is property of a MC. When describing the MC in a continuous state space the simulations still converged to the observed cloud state frequencies. However, introducing spatial dependence this property was not a given anymore.
Since we were unable to reproduce the organizational structure from previous work using the GOES-16 satellite images, we cannot conclude whether it is possible to simulate cloud organization using the MC lattice model. A better understanding of these type of models was achieved. Neighbouring sides could diverge too fast in the performed models. We believe adding a stronger coupling between the cloud state evolution of neighbouring cells can improve the spatial models. Therefore one method to simulate correlated variables was tried to implement on the CTH evolution. This showed promising early results for further research. Also a better correction for horizontal advection on the original images could be performed to observe a specific cloud over time, which could improve the observed data quality.

Om goed te kunnen voorspellen waar, wanneer en hoeveel het gaat regenen is het belangrijk om satellietbeelden, weermodellen en grondmetingen te combineren. Het in 2007 opgezette project 'The Trans-African Hydro-Meteorological Obsevatory' (TAHMO) heeft de afgelopen jaren 500 goedkope weerstations geplaatst, verspreid over 21 landen in Sub-Sahara Afrika en wil uitbreiden naar 20.000 weerstations. De grondmetingen die met de al geplaatste weerstations zijn gedaan, kunnen gebruikt worden om weermodellen te ontwikkelen en te verbeteren.

Over de te verwachten regenval in Afrika is nog weinig bekend. Vaak wordt regen gemodelleerd met een Poissonproces. Daarom is vanuit ‘Delft Global Initiative’ de vraag gekomen of het Poissonproces een goed model kan zijn voor regenval in Afrika.

In dit onderzoek hebben we regendata van één weerstation gebruikt dat tijdens de moesson gegevens heeft verzameld op Mafia eiland, een eiland zo'n 20 kilometer voor de kust van Tanzania.

Een Poissonproces kan homogeen of inhomogeen zijn en we hebben de data op beide processen getoetst. Voor het homogene Poissonproces zijn veel verschillende toetsen te vinden in de literatuur. De Monte Carlo simulaties zijn gebaseerd is op de geïntegreerde verdelingsfunctie en gebruikt om de p-waarde te bepalen. Voor alle regen samen in de gehele observatieperiode was de p-waarde 0 en daarom kan de regen niet met een homogeen Poissonproces worden beschreven.

Voor de inhomogeen Poissonproces benadering hebben we ervoor gekozen om de intensiteit van de regen te benaderen met een stuksgewijs constante intensiteit. Met taut string werd de regen opgedeeld in 474 deelperiodes met een constante intensiteit die per deelperiode verschilt. Voor iedere deelperiode is getoetst of de regen met een homogeen Poissonproces kan worden beschreven. De p-waarde is voor iedere deelperiode bepaald met Monte Carlo simulaties en we werken met een significantieniveau van 5%. Voor 448 van de 474 deelperiodes kan de regen met een homogeen Poissonproces worden beschreven.

Een inhomogeen Poissonproces met stuksgewijs constante intensiteit lijkt daarom een redelijk bruikbaar model om de regen op Mafia eiland mee te beschrijven. Of dit model ook bruikbaar is voor alle andere weerstations van TAHMO zullen toekomstige studies moeten uitwijzen.

When a second tumor arises in the contralateral breast in a patient with a previous or synchronous breast cancer, it is of clinical importance to determine if this tumor is a new unrelated tumor or a metastasis, i.e. clone, of the primary tumor. A new, unrelated tumor may be treated similarly as the first one since treatment was successful, while a distant metastasis demands a change of therapy and has a more adverse prognosis. In clinic, a second tumor is generally regarded as a new primary. If there is clinical suspicion that the second tumor may be a metastasis, clinico-pathological characteristics of the two tumors are used assess the clonality status. Clinico-pathological characteristics, however, are not reliable predictors to determine if a second tumor is a metastasis. Recent studies have investigated tumor clonality using techniques from molecular genetics. These models appear to perform well, but have several drawbacks.

In this thesis a more advanced classification model is being developed that can detect tumor clonality based on SNP array data. For this, two segmentation algorithms, ASCAT and OncoSNP, and two comparison methods, Log LR and adapted SI, have been incorporated. For each tumor, the segmentation algorithms construct a copy number profile based on the SNP array data. Given the copy number profiles, the comparison methods compute a p-value which reflects the probability that a pair is of clonal origin. Both comparison methods are permutation methods which test the null hypothesis of independence against the alternative hypothesis assuming clonality. The proposed model consists of a decision tree which assigns each pair to one of six categories depending on the significance of the four resulting p-values.

The model has been tested on 23 fresh frozen pairs by means of expert judgment. The results were promising: the four pairs which were unanimously labeled as clonal by the experts were also regarded as such by the model. No independent pairs were assigned as clonal by the model. Moreover, the decision tree showed to have a higher sensitivity than the clinical assessments as the latter only managed to detect two out of four clonal pairs. A discordance between the clinico-pathological judgments and decision tree results was found for three out of 18 pairs for which both assessments were available.

The model appears to be suitable in practice, but is not yet applicable as a stand-alone model. There were two ambiguous pairs which were labeled as independent by the model but for which the experts had varying opinions about the clonality status. Until the ambiguous pairs can be reliably categorized, it is advised to take into account both the model results and clinical assessments when determining tumor clonality. Finally, the performance of the model remains to be tested on FFPE pairs.

The goal of this thesis is to implement and experiment with a Bayesian way of estimating a (smooth) monotone regression function by applying it to climate data. The method we use is proposed by Neelon and Dunson. This method uses a piece-wise linear model for the unknown regression function and enforces the monotonicity constraint by the specification of the prior distribution of the slopes. This thesis is also aimed at providing solutions to specific problems that we encounter during the process of applying this method. We encounter two main problems: a numerical problem and a boundary problem. The numerical problem concerns a fraction of very small numbers, which we can solve using an asymptotic approximation of the Mills Ratio. The boundary problem appears in the form of a steep upward-sloping curve at the left boundary. We provide a pragmatic solution to this boundary effect, in which we use an extension of the data set, to obtain a better curve estimate at this boundary.

As Machine Learning models are being applied to a wide range of fields, the potential impact that these algorithms can have on people's lives is increasing. In a growing number of applications, such as criminal justice, financial assessments, job and college applications, the data points are indeed people's profiles. Therefore, in the presence of such sensitive attributes, the risk for algorithmic predictions leading to discrimination should be carefully addressed. Among the state-of-the-art methods aiming at solving such complex problems by taking fairness into account, path-specific causality-based methods are selected in this work. In fact, causality-based fairness metrics are acclaimed in the literature for satisfactorily capturing unfairness in Machine Learning models. In this work, selected state-of-the-art causality-based methods and metrics are compared, emphasizing the methodological and experimental differences between individual- and population-level fairness approaches. Based on these results, a novel method Conditional Path-Specific Effect (CPSE) is proposed, with the goal of bridging the two different approaches by leveraging the properties of conditional Path-Specific Effects. CPSE is tested in comparison with other state-of-the-art methods, both on simulated and empirical datasets. The results suggest a high potential of CPSE for successfully detecting and correcting unfairness.

For modelling microstructures of materials the Voronoi diagram is one of the most commonly used models. In this thesis we study a generalization of Voronoi diagrams known as the Laguerre-Voronoi diagram. In particular, we consider the stereological problem of estimating the 3D cell volume distribution of such a diagram from one of its 2D planar sections. This problem is not in general solvable for all Laguerre-Voronoi diagrams. We consider a specific class of Laguerre-Voronoi diagrams generated using an algorithm which allows to control the volume distribution of its cells. Inspired by related stereological problems, an estimator for the distribution of areas observed in a planar section is proposed. This estimator can be used for estimating the cell volume distribution from a sample of observed areas in a planar section of a 3D Laguerre-Voronoi diagram. Given that the problem is motivated by a materials science application we consider Laguerre-Voronoi diagrams with a lognormal cell volume distribution, which is commonly used in this field. The simulations show that the proposed method works well in the sense that on average the estimated parameters of the lognormal cell volume distribution are close to the actual parameter values. While the focus is on the lognormal distribution, generalization of the estimator considering other parametric distributions is briefly discussed. The thesis is concluded with a case study: the 3D grain volume distribution of a real steel microstructure is estimated from observed areas obtained from 2D image data.

Porous asphalt resides on most top layers of Dutch roads. Scheduling maintenance for these roads is generally dependent on several factors, but ravelling, the loss of aggregates in the top layers, is the main reason for maintenance on Dutch roads. With the recent framework of the DOS-LCMS scheme generating values for aggregate loss in percentages, a prediction for the remaining lifetime of a road section surfaced with porous asphalt with respect to ravelling can be performed. The lifespan for porous asphalt layers is dependent on the most suffered 25% of the section on the respective 100 meter length.
The current threshold is set at 10%, implying that road sections of 100 meter need maintenance if more than 25% of the road (75^th percentile) measures aggregate loss over 10%. The present work approximates these 75^th percentiles throughout the years using parametric and non-parametric approaches, whereafter the estimates of the 75^th percentiles are used to construct smooth monotonic increasing convex curves. These curves, which are in fact functions built on P-splines, are then used to perform extrapolation and hence predict the dates on which the threshold is going to be surpassed. The study reveals problems in the raw data which is particularly prominent in the sequence of 75^th percentiles, frequently showing a lack of monotonicity and convexity. Putting the monotonicity and convexity constraints on a more granular level were found to be helpful for the predictions and improved the consistency of lifetime predictions over consecutive years.