We consider the problem of online nonparametric regression for signals of length n with total variation at most Cn whose observations are contaminated by σ-subgaussian noise. While there exist many algorithms which achieve optimal performance under the assumption of independent noise, this work focusses on the less explored general case of dependent noise. We focus on the Follow-the-Leading-History (FLH) algorithm, a powerful meta-aggregation method for online learning.
We prove that under mild assumptions of weak long-range dependence, we may apply FLH to m ≈ log n partitioned data streams to mitigate high correlations. We show that the resulting algorithm Thinned-FLH (TFLH) achieves the minimax optimal cumulative error rate of O(n^(1/3)C_n^(2/3)) with high probability, matching the performance in the independent case up to logarithmic factors. We also conduct a simulation study, which validates our theoretical findings and demonstrates that TFLH may outperform FLH in high dependence environments in spite of the data thinning. ... Read more

This thesis examines rainfall event characteristics in the Netherlands over a 26-year period (1998–2023) using radar-derived precipitation data. Extreme precipitation is a major contributor to flooding, which impacts human life, infrastructure, and ecosystems. A life-cycle-based tracking approach is employed to analyse rainfall events in terms of spatial extent, duration, and intensity, using 5-minute precipitation data at a 2.4 km resolution.

The study reveals significant increases in the spatial extent and duration of rainfall events, with these trends persisting across most seasons. Intensity trends are more complex: while shorter-duration events show decreasing intensity, a closer look at smaller-scale shorter-duration higher-intensity events indicates an increase in intensity. No significant changes in the shape parameter of extreme event distributions are detected over the study period.

The analysis also finds strong correlations between event duration and area, and between intensity and both duration and dew point temperature, with these relationships evolving over time. This work provides valuable insights into the dynamics of rainfall events in the Netherlands and lays a foundation for future research on refining intensity metrics, distinguishing rainfall types, and improving flood risk assessments. ... Read more

Accurate modeling of vacuum dynamics in Trailing Suction Hopper Dredgers (TSHDs) is critical for optimizing suction production and mitigating sensor anomalies. This study proposes a data-driven, physics-guided operator learning framework to estimate the vacuum pressure loss parameter θ, a variable derived from physical principles in dredging operations. Leveraging a modified Deep Operator Network (DeepONet), we introduce attention-based interactions between branches and the trunk network to capture complex dependencies in the sensor data. A local trunk mechanism is introduced to preserve temporal locality across dredging trips.
Due to the nature of a lagging density sensor, we integrate a real-time rolling mean error correction mechanism. This addresses training biases for refined predictions, as well as offering an anomaly detection mechanism. The model is trained and validated on real-world vessel data, including synthetic simulations of vacuum processes, and evaluated using trip-wise and global metrics. Experimental results show that the proposed architecture significantly outperforms the rolling mean baseline setups and the classical DeepONet across accuracy metrics such as the root mean square error (RMSE).
This work demonstrates the value of combining domain knowledge with operator learning techniques in maritime engineering. The proposed framework offers a scalable framework, allowing application across entire fleets for real-time suction production estimation and anomaly detection, contributing to efficient dredging operations. ... Read more

This thesis investigates the problem of time-varying function optimization. In particular, we study techniques to minimize the cumulative regret when optimizing a time-varying function in the Gaussian process setting. First, we introduce the problem and present a literature review of the current methods and results. Following this, we we propose enhancements to existing algorithms, demonstrating improved regret bounds. We discuss the applications of these algorithms and where they can provide a benefit compared to existing methods. With these applications in mind we introduce two new temporal models for time-varying functions and their associated algorithms. We test their performance in order to validate their effectiveness and potential benefits. ... Read more

This thesis presents a novel approach to optimize execution strategies in the Foreign Exchange Spot Market, focusing on the application of data-driven methodologies and stochastic modeling.
It begins by proposing a new measure to evaluate the limit order book volume imbalance, which considers multiple price levels and their weighted impact on market predictions.
Then the research employs a combination of convolutional neural networks and long short-term memory models to analyze the limit order book data and its imbalances, i.e. the previously introduced limit order book volume imbalance and the order flow imbalance, which takes into consideration their time evolution. This methodology allows for the exploration of price movements and the identification of optimal execution strategies by predicting future mid-price movements, which are embedded in the drift term of the stochastic model. The findings indicate that the developed models outperform traditional strategies by adapting more effectively to market dynamics.
Further, this work develops a backtesting environment that simulates market conditions to empirically validate the effectiveness of the proposed strategies against historical data. The results demonstrate a superior performance in terms of profitability and cost-efficiency compared to traditional models that do not utilize the drift term from predictive analytics in their stochastic model of the mid-price.
Future work may extend these methodologies to other financial markets and explore prediction models that include the influence of multiple assets. ... Read more

This thesis aims to enhance existing models that infer parameters describing the spread of a virus by analyzing the distribution of empirical cluster sizes of identical genetic sequences. An approach that has gained recent popularity assumes that each individual cluster can be modeled as a Bienaymé-Galton-Watson process, with the distribution of empirical cluster sizes being equal to the law of the final size $\widetilde{Y}_\infty$ of the branching process. By employing the theory of general branching processes counted by characteristics, we demonstrate that the empirical cluster size distribution $C^\alpha$ stochastically dominates $\widetilde{Y}_\infty$ due to the exponential growth of the branching process. Under the assumption that the underlying branching tree follows either a Bienaymé-Galton-Watson process or an age-dependent process, we show that the mean of the empirical cluster size distribution can be used for a (strongly) consistent estimator for the probability of mutation $\nu$. For both branching models, we compute $P(C^\alpha=n)$ for $n=1,2$. We conjecture that $P(C^\alpha=n)$ is independent of the underlying model and that it can be expressed as a function of the mean of the offspring distribution $X$, and the probability mass function of $bin(X, 1-\nu)$. An extension of the model is considered where the probability of mutation is sampled from a distribution $\nu$ for each cluster. We show that under this assumption the empirical mean of the cluster sizes estimates the quantity $\int \nu^{-1}(r) dr$. We also show that the $\nu$ can still be estimated by the empirical mean of the cluster sizes, when the population is divided into a finite number of types with inhomogeneous offspring distributions. ... Read more

The growing demand for renewable energy and the increased installation of wind turbines have brought challenges related to operational efficiency and predictive accuracy. In this thesis, we extend the method 'Narrowest Significance Pursuit' (NSP) to non-linear frameworks and explore the application of Non-Linear NSP to detect multiple change points in wind energy production data. By identifying structural shifts and anomalies, NSP can significantly enhance predictive models used in wind power forecasting. The study introduces two parametric as well as isotonic regression and S-shaped non-parametric models to handle non-linearity in wind turbine data.
The results demonstrate superior performance of isotonic regression over parametric approaches, especially in terms of detecting gradual changes and subtle anomalies. However, issues like model misspecification and computational inefficiency remain, prompting further optimization efforts. We also recommend expanding NSP methods to other renewable energy sectors, such as solar energy, to broaden the applicability of these models. ... Read more

With the ever-increasing need to reduce the use of fossil fuels, Tesla is accelerating the world's transition to sustainable energy. This means replacing all internal combustion vehicles with electric ones over time. The growing number of Tesla vehicles on the road poses interesting scaling challenges for all departments especially for the Service Engineering team. To help prioritize issues and reduce service costs, frequencies, and duration, a way to generate an overview of all the costs separated by types of repair is needed. This thesis aims to automatically generate such an overview by borrowing techniques used in Natural Language Processing. In particular, the LDA and GSDMM algorithms for topic generation are tested. Additionally, a novel method based on the cross frequencies of items is presented. Methods are also presented to compute the novelty of every topic and a new metric, here called the growing score, is introduced as a mean to monitor the frequencies of the topics over time. The methods are applied to service records data from Tesla and the results are analyzed in detail. The results are also enhanced by computing additional information regarding costs for all parts of the service visit and also the configurations of the cars. It is found that the novel approach for the topic generation and the novelty and growing scores produce useful information that can be used to optimize and avoid the need for service procedures to reducing total cost of ownership. ... Read more

The Bayesian approach is a very important approach for tackling problems in statistics. It involves choosing a distribution that reflects the prior knowledge and  thus takes all knowledge into account in contrast to the frequentist approach. It also assumes that the parameters (the regression coefficients) follow a distribution called the posterior distribution instead of fixed constants. When a specific choice of this prior is made, this needs to be justified as the prior directly influences the posterior distribution of the regression coefficients. It is also possible to consider priors that do not carry a lot of information and such priors will be compared in this project. 

In this thesis, the Bayesian approach will be used to apply a multinomial logistic regression model to data concerning students’ study habits and beliefs. The data is provided by a research group called PRIME and they focus on mathematics education at the TU Delft. Multinomial logistic regression is used to find predictions of the choices expressed in probabilities. Bayesian statistics is not only useful in a sense that it offers the possibility to specify the prior knowledge, but also because the Bayesian way of thinking can be incorporated in evaluating results. This can be done by constructing credible intervals for the predicted probabilities. Overlap between intervals can then give insight on prediction quality.

In this project, the models are coded in R and here two packages are used: the UPG and the BRMS package. The priors that are compared are the Gaussian and Cauchy distributions. Other than that there are also default priors used in the packages, which can be compared to the Gaussian and Cauchy priors. In the end, a conclusion can be drawn about the performance of each model based on the prediction accuracy. It can be concluded that the BRMS package outperforms the UPG package in terms of accuracy both using default priors and overall using default priors gives more accurate results than specifying the prior. However, the difference in the accuracy of the model using the BRMS package is not significantly higher than the accuracy obtained from the UPG model and the running time is a lot higher for the BRMS package. From the models with a specified prior, the model with the Cauchy distribution as prior performed better. ... Read more

This study examines the validity of constant failure rates in the reliability assessment of storm surge barriers, with a focus on the Stormvloedkering Oosterschelde (SVKO). Analysing a dataset of 1,501 malfunctions, including 87 critical incidents over six years, we employ Exponential and Weibull statistical models to assess failure rates. The research question—whether the assumption of constant failure rates over time is valid—is addressed with a nuanced perspective. The findings in this study reveal that neither model conclusively fits all failure scenarios, with some data supporting constant rates and other data indicating variability. The Weibull model better describes certain scenarios, suggesting variable failure rates, while in other instances, both models show comparable performance. The p-values from hypothesis testing and visual inspection of component data provide inconclusive evidence, leading to the suggestion that both constant and variable failure rates may exist in storm surge barrier components. The research contributes to the field by challenging the prevailing assumption of constant failure rates, developing a statistical framework, and by suggesting the need for a flexible, scenario-specific approach to modeling failure rates for improved reliability assessments. ... Read more

De 'grootte' van een verzameling staat in de wiskunde bekend onder de term 'kardinaliteit'. Omdat de kardinaliteit van de natuurlijke getallen niet met een eindig natuurlijk getal n kan worden aangetoond, is de kardinaliteit van deze verzameling uniek gedefinieerd als alef-nul. Met dank aan Cantor’s bewijs voor de stelling dat de verzameling reële getallen overaftelbaar is, weet men dat er verzamelingen bestaan met kardinaliteit groter dan alef-nul. De eerstvolgende verzameling die groter is dan de verzameling natuurlijke getallen geven we kardinaliteit alef-één. 
Vanzelfsprekend zijn er voor verzamelingen met kardinaliteit alef-nul talloze mooie stellingen geformuleerd en bewezen. Deze stellingen kunnen eenvoudig worden uitgebreid naar verzamelingen met kardinaliteit alef-één, door de term 'eindig' in 'oneindig' te veranderen en 'aftelbaar' in 'overaftelbaar'. Het valt echter op dat sommige stellingen die gelden voor verzamelingen met kardinaliteit alef-nul niet meer gelden nadat ze zijn uitgebreid naar verzamelingen met kardinaliteit alef-één. Het kan ook gebeuren dat een stelling juist wel in het overaftelbare geval geldt, maar niet in het aftelbare geval. In dit verslag zullen een aantal dergelijke stellingen aan bod komen.
... Read more

Improving data quality is of the utmost importance for any data-driven company, as data quality is unmistakably tied to business analytics and processes. One method to improve upon data quality is to restore missing and wrong data entries. 

The goal of this research is construct an algorithm such that it is possible to restore missing and wrong data entries, while making use of a human adaptive framework. This algorithm has been constructed in a modular fashion and consists of three main modules: Data Transformation, Data Structure Analysis and Model Selection. Data Transformation has concerned itself with conversion of raw data to data types and forms the other modules can use.

Data Structure Analysis has been designed to deal with correctly missing data and dichotomy in the target feature by making use of three clustering algorithms: DBSCAN, K-Means and Diffusion Maps. DBSCAN is used to determine the necessity of clustering as well as the initialisation of the K-Means algorithm. K-Means and Diffusion Maps have been used as clustering methods in the one-dimensional target feature and the two-dimensional input-target feature pairs, respectively. Data Structure Analysis has further been designed to perform feature selection through three filter methods: CorrCoef, FCBF and Treelet.

Model Selection has proposed a novel approach to selection of the best model of a candidate set through the optimisation of a conditional model ranking strategy based on the prior construction of theoretical testing. Our candidate set consisted of Expectation Maximisation, K-Means, Multi-Layer Perceptron, Nearest Neighbor, Random Forest, Linear Regression, Polynomial Regression, ElasticNet Regression.

In terms of restorability, it was shown that the optimal configuration of the Cleansing Algorithm for the restoration of missing data, was provided by opting not to use clustering, using a custom alteration to the Treelet algorithm for feature selection and making use of the model selection strategy. This not only lead to the greatest restorability of 56.90% on Aegon data sets, which was an improvement of 44.83% when compared to not using the Cleansing Algorithm, but also to the reduction of computation time by over 400%. A more realistic restorability due to the presence of correctly missing data, was given by the same configuration making use of one-dimensional output clustering. This resulted in a restorability on Aegon data sets of 43.10%. As such it was deemed possible to restore missing data on Aegon data sets.

With respect to the human adaptive framework, it was determined that the construction of the algorithm be modular in the sense that any alternate feature selection or clustering approach can be implemented with ease. Furthermore, the model selection module allows us to customize the theoretical testing and choice of regression or classification models for the restoration of missing data. In doing so, the algorithm has laid the foundations for human adaptivity of the Cleansing Algorithm. ... Read more

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

The goal of this report is to present and describe the effort surrounding the completion of the Master Thesis Project of classification in football. Classification is a procedure which belongs in the field of Statistics. The objective is to capture, detect and distinguish certain actions relative to the environment of analysis. In our case we are focused on classification for actions related to football, using sensor data. As a first step we introduce the motivation that enforces our project and also the nature of the sensors that provide us with the information for our analysis. We follow with some enlightening review of previous research on motion recognition related projects, in order to have some supplemental information that will provide us with experience that will serve as guidance and further direction. Afterwards we introduce the methodology of the classification. The methodology includes all the models and tools needed to achieve a precise and robust classification outcome. As a next step, we dive through the details of the experiment we are going to analyse, while we explain the process followed in order to create a refined data set that will consist the input of our models. After the description of the data and the preprocessing procedure, we present the results obtained by the analysis along with the evaluation and relative comparisons. Finally, we give the most important conclusions we reached in the whole process along with some proposals for future improvements. ... Read more

Currently, speaker recognition research is mainly based on phonetics and speech signal processing. This research addresses speaker recognition from a new perspective, analysing the transcription of a fragment of speech with text analysis methods. Since text analysis is based on the transcription text only, it can be assumed independent from current automatic speaker recognition software. Hence, it would contribute significantly to the overall evidential value. The analysis is based on the frequencies of non-content, highly frequent words. We study whether information about the identity of the speaker is contained in the transcription of spoken text. The value of evidence is quantified using a score-based likelihood ratio. The score-based approach is chosen because in most forensic cases, there is not enough data from the suspect or of the disputed speech fragment available to model a robust feature-based likelihood ratio. Different methods to model the system from feature vector over score to likelihood ratio have been compared. As a baseline, a distance based method is used, where the score is the distance between the feature vectors. To improve upon this baseline, machine learning algorithms are implemented. The results from SVM and XGBoost are explored. As a third method a feature-based likelihood ratio is calculated and used as a score instead of as a direct likelihood ratio. With this method, both similarity and typicality are taken into account. The model is trained and tested on the FRIDA data set from the Netherlands Forensic Institute, consisting of Dutch conversations from a homogeneous group of 250 individuals. The performance of the likelihood ratio system is evaluated through computing the cost log-likelihood-ratio (Cllr), which is a measure for the accuracy and quality of the likelihood ratios, and the accuracy (A) of the likelihood ratios solely. The performance is also evaluated by inspecting the Tippett, empirical cross-entropy and pool-adjacent-violators plots. Different values for parameters used in the calculation of the likelihood ratios are investigated: the length of the sample, the number of frequent words (number of features) and the number of samples needed to train the model. The distance method showed a strong baseline, with good performance for large sample lengths. The SVM method outperformed the distance method for all parameter settings, with a peak performance of A=0.94 and Cllr=0.24. The XGBoost method showed promising results for smaller samples lengths, but a too large amount of data is needed to obtain good performance for larger sample lengths. The LR score method showed moderate results, but no improvements due to the necessity to estimate high-dimensional distributions. This thesis shows that information about the identity of the speaker is contained in transcriptions of speech. The complete process from data to likelihood ratio is constructed, where the likelihood ratio quantifies the evidential value of a transcribed speech fragment. ... Read more

In order to provide accurate statistics for industries, the classification of enterprises by economic activity is an important task for national statistical institutes. The economic activity codes in the Dutch business register are less accurate for small enterprises since small enterprises are not labelled manually. To increase the quality of the register, automatic classification of enterprises based on their websites has been tried with supervised text mining techniques. The performance of current supervised text mining techniques is limited by the available accurately labelled training data. Since inaccurate labels are available for all enterprises, the current study investigates how to leverage the noisy labelled data to improve the economic activity classification of small enterprises based on their webpage texts. The current study compares the performance of various semi-supervised methods that enlarge the training data by leveraging the abundance of noisy labelled data. The methods are compared against a supervised baseline, which uses all noisy data as is. The proposed proportional weakly self-training method queries noisy labelled instances through high probability sampling and filters mispredicted instances. Results showed that proportional weakly self-training improves upon the supervised baseline while requiring far less training instances. From qualitative analyses, we conclude that the filter of proportional weakly self-training reduces error propagation compared to classic self-training. Additional experimental results showed that large enterprises are less suitable as training data for prediction of small enterprises and that top-k performance scores improve results but are not yet sufficient for semi-automatic classification. Further examination of error detection methods is recommended to improve web-based economic activity classification. ... Read more

Sinds 2015/2016 krijgen de leerlingen op de havo met wiskunde A op hun eindexamen een blad met enkele vuistregels. In deze thesis heb ik de achtergrond van deze vuistregels onderzocht en de vuistregels zelf tegen het licht gehouden. ... Read more

What is the actual value of a house and which factors contribute the most to it? In this thesis we do a thorough research and try to come up with an answer. We will set up models that approximate the current market values for all houses in the Netherlands. To do this, we use a lot of data from different sources. Various characteristics of houses, the location and the trend on the housing market will be used.
... Read more

This thesis is dedicated to the application of data science to sports data. The research for this thesis is part of a bigger project on injury prevention and sport performance called Citius Altius Sanius (CAS). Two data sets from two different projects within CAS are analysed, with two different goals; one focusses on sports injury prevention in soccer, the other on performance prediction in baseball. First we analyse a data set on acceleration during exercise from project P6, generated while testing a prototype of wearable sensor trousers during soccer drills. The aim of P6 is to design special leg wear with wearable sensors in order to gain more knowledge on hamstring injuries. Therefore, an algorithm needs to be developed to identify the intensity of certain movements using sensor data. Features were extracted from the acceleration data in order to classify the intensity. Four methods are then tested on the data, of which the decision tree seems to produce the best results. Analysis showed that this model seemed to be able to predict low intensity well (99.1% accuracy), although it struggles signicantly more with medium and high intensity exercise (75.5%). The second data set covered the growth in throwing speed of a group of young baseball athletes between the ages of 12 and 18. The aim of the research was to identify a common growth curve for throwing speed of pitchers during adolescence and provide personalised growth curve models. A mixed effects or multilevel design was chosen to model the growth in throwing speed, due to its ability to model the hierarchical nature of the longitudinal data. After analysing the data set and covariates, we found we could reduce the number of predictors, and thus the cost of collecting data. Furthermore, it is possible to predict throwing speed on a personal level using only age and one measurement on the predictors and throwing speed, although predictions are improved when more measurements are available. The results of this research can be implemented in the projects, although some complications and opportunities for improvement still exist. Recommendations for future research have therefore been discussed. ... Read more

In this report, inhomogeneous Lévy processes are studied in a discrete observational model based on derivatives of the process. First, homogeneous Lévy models are defined and an already known nonparametric method, using Fourier techniques and call and put option prices, for estimating the parameters of the model is described based on Belomestny and Reiẞ (2006a). Previous research suggests that there is a need for an extension of this concept since option prices with different maturities produce significantly different results. After all, the assumption that the parameters of the model are the same for any time window is not realistic and better results could be achieved once this premise is rejected. That is why inhomogeneous Lévy processes are introduced and studied in this report. The estimation method for the homogeneous model from Belomestny and Reiẞ (2006a) is extended to fit into the inhomogeneous framework. Next, asymptotic normality of the estimators is proven for these processes in this setting and confidence intervals are constructed using the finite sample variance method. Asymptotic normality has already been shown and confidence intervals have been constructed in the homogeneous framework in the continuous observational model by Söhl (2014). Finally, data is simulated from an inhomogeneous Merton model to test the performance of the method and options from the S&P 500 index are used as a real-world application. ... Read more