In this thesis we develop statistical methodology for stereological estimation problems which in particular appear in the field of materials science. We study mathematical models which may describe materials microstructures, and we develop statistical methods for estimating the parameter(s) of these models in a stereological setting. That is, typically we consider a 3D model, and instead of directly observing data generated by this model we only observe a 2D planar section. In many cases we even consider (𝑑 −1)-dimensional sections of a 𝑑-dimensional model (𝑑 = 2, 3, . . . ), because it turns out this is often not more complicated than the 𝑑 = 3 case. In order to formally define and study these models we mainly rely on concepts from stochastic geometry and point process theory. This thesis is divided into two parts. In part I we consider a model of randomly positioned and -oriented particles of the same shape, but varying in size, and in part II we consider a space-filling model by studying a random tessellation (mosaic). In these models, the particles of a particle process, or the cells of a random tessellation, may represent the so-called grains of a materials microstructure....

In this report the uniform deconvolution problem will be discussed. It is a statistical problem where the observations we would like to make are distorted by an independent additive noise sampled from a standard uniform distribution. The sampling density is therefore the convolution of the distribution function of interest and the standard uniform density. However, we would like to know the distribution of the data without the uniform convolution, or in other words, we want to infer the deconvolution of the distribution of the observables by the uniform density, based on the observable noisy data. We will first define this problem mathematically and find a connection between the distribution of the observed data and the distribution that we would like to know. Having constructed this relation, we aim to estimate the unknown distribution based the noisy observations. It turns out that this problem is related to the current status problem. This is a problem in which patients are tested for a disease to find out the time of onset of the disease. However, the observations only tell us whether patients are infected or not at the time of the test, but not the time of onset of the disease. We would like to know the times of onset as we can use these to estimate the distribution of the time of onset. To estimate this distribution, we will use the connection to the to the uniform deconvolution problem. Thus, when the relation between the distribution of the observations and the unknown distribution of the variables of interest is created, we would like to estimate the distribution function only using finitely many noisy observations. To estimate this, estimators like the MLE or MoM cannot be used as we would need to assume that the family of possible distributions can be parameterized smoothly by a Euclidean parameter. In our case, the family of possible distributions is much larger and does not satisfy this assumption, so we have to use nonparametric estimation methods. We will show two different methods of this nonparametric estimation; the nonparametric maximum likelihood estimator and the kernel density estimator. For the nonparametric maximum likelihood estimator, we first constructs the (log-)likelihood function of the problem and then we maximizes it over all possible distribution functions in the allowed family. This maximizing function is defined as the NPMLE. There is not a general method to obtain this distribution so we will have to use specific properties of our problem. Then we will use the method of isotonic regression to obtain the maximum likelihood estimator for the unknown distribution function. The other method that will be used to estimate the unknown distribution in a nonparametric way is kernel density estimation. This method constructs a distribution function more directly than the NPMLE. The intuition behind this estimator is simple, if there are a lot of observations near a value, the probability density in that value should be high, and the other way around. Finally, we will simulate the uniform deconvolution problem and solve it using the two discussed methods. The methods and their respective strengths and limitations will be compared. The kernel density estimator turns out to give a more smooth and accurate estimate but depends on an optimally chosen parameter which, in practice, cannot be calculated exactly and differs from case to case. The nonparametric maximum likelihood estimator does not depend on any parameter and the way of calculating it is the same in every case, but is only able to produce step functions.

Over the last decade, an increasing amount of data has become available for data analysts to understand. Datasets containing books, images, networks, or other types of data have been studied. A recent group of methods proposes to analyze samples in datasets based on a description of their shape. This group of methods is often referred to as Topological Data Analysis (TDA). In this thesis, an extension to the most commonly used TDA method, called Persistent Homology (PH), is proposed. PH only describes topological features, while this extension additionally allows for the description of geometric properties. The new information is obtained via the persistent Laplacian, a recently proposed operator that encodes the topological information of persistent homology in its kernel and geometric information in its non-zero spectrum. The persistent Laplacian contains a lot of information and extracting the relevant parts has not yet been standardized. In this thesis, a new operator, the persistent multiplicity operator, is proposed. The new operator summarizes the information of the persistent Laplacian such that it can easily be extracted and used to extend PH. This allows the many previously studied methods based on persistent homology to additionally describe geometric properties, as opposed to only topological features. For the multiplicity operator, the trace is analyzed and the features captured by it are discussed. Besides analyzing the sum of the eigenvalues, it is argued that individual eigenvalues could contain more information. However, these are deemed hard to understand. Therefore, an adjusted multiplicity operator is proposed that contains separately interpretable eigenvalues. Finally, the operators are used to classify handwritten digits from the MNIST dataset and to make statistical tests that can detect different generation processes of artificially made cross sections of crystalline structures.

This thesis investigates long-term climate trends in the Netherlands using historical weather data from the De Bilt station, maintained by the Royal Netherlands Meteorological Institute (KNMI). It examines changes in temperature, precipitation, and extreme weather events, including tropical days, ice days, and days with heavy or minimal rainfall.

To identify trends, both continuous variables (e.g., annual average temperature) and count-based indicators (e.g., number of tropical days) are analyzed. Methods include linear and isotonic regression for continuous data, and Poisson and negative binomial regression for count data, which often show overdispersion or excess zeros. Hypothesis tests, including slope tests and permutation tests, are used to assess statistical significance.

Results show strong evidence of warming: yearly, winter, and summer temperatures have all increased, with a clear rise in tropical days and a decline in ice days. Precipitation trends are less pronounced but suggest increases in winter and annual totals. The frequency of dry, wet, and extremely wet days also shows modest upward trends.

Overall, the findings confirm that regional climate change is observable in Dutch weather records. The results are consistent across multiple statistical models and align with global observations reported by the IPCC. This study contributes to the understanding of how global climate shifts manifest at a local level.

Accurate early prognostication after pediatric cardiac arrest is clinically crucial yet remains methodologically challenging. This thesis frames the problem as a representation learning task on raw electroencephalography (EEG) and introduces a fully self-supervised pipeline followed by a supervised classifier. A Time-Series-to-Vector (TS2Vec) encoder is trained on 6,669 unlabeled twenty-second EEG epochs (T = 2000 time points, C = 4 channels) from 84 comatose children treated at Erasmus MC Sophia Children’s Hospital. The encoder learns to map each EEG epoch to a 320-dimensional vector by contrasting transformed views of the same signal from unrelated signals, without using outcome labels.

Downstream classification is performed with a k-nearest neighbors (k-NN) model. Probabilities are assigned at the epoch level and aggregated across all epochs of a patient to generate a final patientlevel prognosis. Five-fold patient-level cross-validation gives an area under the ROC curve of 0.861 ± 0.092, an accuracy of 0.774±0.045 and an F1 score of 0.733±0.057. Critically, specificity and precision are both 1.000 ± 0.000. Thus the model never predicts death for a child who survives, satisfying a stringent clinical safety requirement. Sensitivity is 0.581 ± 0.070, reflecting a deliberately conservative decision threshold.

Qualitative analyses offers tentative support for the physiological relevance of the learned features. t-SNE projections show clustering by patient identity and good separation between the two extreme EEG background patterns (continuous normal activity and electrocerebral silence) without supervision. Saliency analysis did not yield clinically interpretable patterns.

Compared to the leading feature-engineered qEEG baseline, the proposed approach achieves equivalent specificity and a slightly lower AUC, while removing the need for manual feature design and expert annotation. The modular architecture invites several extensions, including graph-based encoders that respect electrode topology, integration of auxiliary data such as ECG and clinical metadata, retrieval-based reasoning using large historical EEG archives, and more interpretable or end-to-end trainable models. Overall, this work demonstrates that contrastive learning can be effectively applied to raw pediatric EEG for conservative, label-efficient outcome prediction after cardiac arrest, and offers a mathematically grounded proof of concept for future clinical applications.

Progressive familial intrahepatic cholestasis (PFIC) is a group of rare, inherited liver diseases that affect children and are characterised by impaired bile flow. Since PFIC is a paediatric ultra-rare disease, conducting randomised controlled trials is particularly challenging, making observational data essential for improving clinical management. This thesis analyses a large multinational observational retrospective data cohort with long-term follow-up of PFIC patients. The aim is to improve our understanding of PFIC and support more informed decision-making in patient care through the investigation of two key aspects of disease monitoring and progression. First, the thesis explores longitudinal trajectories of relevant biochemical parameters, serum bile acid levels and platelet counts, in patients with a specific subtype of PFIC, PFIC2, using latent class linear mixed models. This approach effectively identified distinct longitudinal patterns of serum bile acids and platelet counts in patients with PFIC2. These patterns highlight significant heterogeneity in the progression of laboratory parameters over time. Second, a comparative analysis of event-free survival is conducted between two European regional cohorts of PFIC patients, North-West Europe and South-Central Europe. Hypothesising that there are no differences in event-free survival of PFIC patients despite different care settings. This is achieved through a weighted survival analysis combining inverse probability treatment weighting with the Kaplan-Meier estimator and the Cox proportional hazards model. The results suggest there are no significant regional differences in event-free survival among PFIC2 patients between the two cohorts. Furthermore, a sensitivity analysis and permutation test have been performed, which also support this result. Together, these findings contribute to a more detailed understanding of disease progression in PFIC patients and provide practical tools and insights that can inform patient monitoring and clinical decision-making in the absence of randomised trials.

This thesis develops a mathematical and computational framework for demand sensing in supply chain management, addressing the dual challenges of forecast accuracy and hierarchical coherence. This work was carried out during a graduate internship at Dassault Systèmes. Modern retail demand is shaped by vertical aggregation constraints, horizontal product interactions, and temporal dependencies influenced by external drivers. Traditional approaches (classical time series, machine learning, and reconciliation heuristics) treat these aspects separately and struggle to deliver coherent and accurate forecasts at scale.

The thesis first establishes a theoretical foundation for multi-product demand forecasting. Forecasting is formalized as a supervised learning problem on probability spaces, introducing the multi-product demand process and a general forecast operator that unifies local versus global modeling, recursive versus direct horizons, and alternative loss functions. Hierarchical forecasting is expressed in compact linear algebraic form, showing how classical heuristics and optimal reconciliation (MinT/OLS) can be understood as projections onto the coherent subspace.

Building on this, the thesis introduces a graph-based extension of the framework. By embedding time series into relational graphs, Graph Neural Networks (GNNs) capture vertical, horizontal, and temporal dependencies within a unified model. An end-to-end forecasting pipeline is proposed, combining graph construction, feature extraction with external covariates, GNN encoding, and forecast generation, with coherence ensured through bottom-up construction, regularization penalties, or post-hoc reconciliation.

Empirical evaluation on the M5 dataset demonstrates the practical implications. Incorporating external drivers consistently improves accuracy across models and aggregation levels. Machine learning models, particularly gradient boosting, outperform classical baselines at granular levels, though the latter remain competitive at higher aggregations. The proposed Hierarchical Graph Network (HGN) achieves competitive results, with particular benefits at intermediate levels where both hierarchical and cross-series relations are most informative. A comparison of local versus global training highlights the trade-off between accuracy and computational efficiency.

The findings underscore three insights for practice: external drivers require robust data infrastructure, hybrid local–global modeling offers balanced accuracy and efficiency, and reconciliation remains essential to guarantee coherence. Overall, the thesis demonstrates how integrating hierarchical structure, external signals, and graph-based learning advances both the theory and practice of demand sensing in modern supply chains.

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.

The main concern of this thesis is applying statistical methods to tackle some issues that arise from specific cases where data are hard to obtain, spatiotemporal, or non-normal. The range of such potential applications is huge. These hard-to-solve problems often necessitate innovative strategies, prompting the development of novel statistical models and methods. While the subjects covered in this thesis are diverse, they consistently revolve around the modeling methods in Statistics for complicated data structures, where traditional methods fail to provide viable solutions. Among the topics presented, we have the optimization for a computationally expensive black-box function based on limited data; predicting a spatiotemporal flow at a new input using the data stored as a tensor; the evaluation of a manufacturing process considering non-normal data and asymmetric tolerances; and, in the presence of dependence structures, defining the joint distribution of multivariate Poisson counts.

In this thesis, we separate all topics into two kinds of issues and propose several tailored statistical methods. First, we consider the case where the process of acquiring data is intricate.
Two specific examples are considered, including the optimization for black-box functions and the prediction for spatiotemporal flows. In these two cases, data are both expensive and time-consuming to obtain. Therefore, the key is to achieve specific goals while minimizing collection costs. We design proper inputs to feed and apply the Gaussian process model as a surrogate model. Then, some customized methods are employed. For black-box functions, where no explicit expression is available, the optimal approach is to select inputs that are as close as possible to the true optimum. Thus, a sequential design based on Gaussian process models is conducted.
It will explore the whole feasible region and find a local area close to the true optimum, only based on limited inputs. Then, more points will be chosen over this region to find the optimum.
When predicting flows, the scenario is notably distinct due to the multi-scale nature of the limited data in both spatial and temporal dimensions, which are typically collected and represented as a tensor. Directly applying surrogate models is not feasible because there are plenty of data observations for training, leading to extremely high computational complexity.
To handle such data, a tailored multi-output Gaussian process via a compression method is used to extract spatial and temporal basis functions, along with low-dimensional input-dependent coefficients, respectively. Then, surrogate modelling is implemented based on input-dependent features, allowing for accurate and fast predictions of unobserved flows.

Next, we address the challenge of analysing non-normal data, which includes both continuous and discrete scenarios. The former occurs when assessing the manufacturing processes, and the latter involves analysis of multiple dependent Poisson counts. We handle non-normal distributions based on the following fact: applying the cumulative distribution function (CDF) of a random variable to that random variable yields a uniformly distributed random variable on $[0, 1]$, assuming that this CDF is continuous. When evaluating a manufacturing process, some data on a characteristic of interest are collected first. Then, the process capability indices (PCIs) can be calculated for the quality control. We focus on the case where there are asymmetric tolerances to define PCIs, and the characteristic follows an unknown continuous univariate distribution.
Two tailored PCIs are proposed, with an inverse transformation introduced to handle non-normal data. We estimate the underlying CDF of the data via B-splines, transforming the data to be normal. Then, our PCIs can be used to assess the capability of an in-control production process in manufacturing conforming products based on non-normal data. Furthermore, when dealing with multiple Poisson counts, it is essential for both the marginal and joint model specifications to accurately capture the random behaviour of the variables. Although there has been a growing interest in this type of data across various scientific fields, models that account for multivariate Poisson distributions remain relatively uncommon. To address that, we introduce a novel multivariate Poisson distribution, leveraging multivariate reduction technology and copula methods, which offers unprecedented flexibility in modelling joint distributions and dependence structures. Various probabilistic properties and several estimation techniques are also explored.

In summary, this thesis makes significant contributions to the field by advancing statistical modelling techniques, particularly in addressing complex and challenging data scenarios.

As technology advances, more industrial devices are achieving higher reliability and longer lifespans. However, challenges such as limited sample sizes of experimental data and the complexity of factors influencing device degradation are becoming increasingly prevalent. Simultaneously, abundant degradation information from other data sources, including data from other components, historical batches, and different experimental stress levels, is available. Thus, there is an urgent need to find ways to fully utilize these multi-source data for industrial device reliability analysis. Therefore, this thesis proposes several data fusion methods to perform the reliability analysis of industrial devices that collect degradation data from different sources. The research addresses three primary research objectives: developing a data fusion-based framework for predicting the remaining useful life (RUL) of industrial devices that collect multivariate sensor data, formulating reliability analysis methods for degradation data from different batches of industrial devices, and establishing a framework for analyzing degradation data under varying experimental stresses and stress levels....

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

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.

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.