Accurate capacity planning is essential to ensure uninterrupted services and network stability through peak hours for the transport core network of KPN. This involves a trade-off between minimizing the risks of capacity shortages and costs of capacity expansions. High network loads are occurring more frequently and their magnitude is increasing. This necessitates measures to foresee high load situations before network capacity is surpassed. Currently, planning is based on manual predictions that lack substantiation. This research aims to improve network capacity planning by development of a forecast for the next year.
An analysis of the daily maximum traffic data of the transport core is performed, to determine the most suitable models for the prediction of network traffic. The data analysis, employing time series decomposition, revealed non-stationary trends and annual seasonality; traffic decreases throughout the summer and increases in the winter. An upward trend in the frequency and intensity of traffic peaks, highlights the growing demand and shifts in usage behavior. The extreme traffic peaks in the historical data were correlated to F1 race days and other anticipated events.
Two algorithms that integrate exogenous variables were assessed to predict the extreme values. The models either yielded inaccurate traffic predictions or encountered challenges in interpretability and pattern recognition, with the limited amount of data available. In response to these limitations, a decomposed forecast was created that predicts the trend and seasonality. Furthermore, Extreme Value Analysis (EVA) was implemented to address the extreme values in the data.
The final prediction framework combines the decomposed forecast with EVA for the next six quarters and outperforms the other models. The model effectively captures extreme values and provides insights into the maximum expected peaks and risk levels. The substantiated forecasts of the EVA model and the manual predictions yielded comparable results. However, the EVA model provides better insights into the likelihood of exceeding specific traffic values, which enhances capacity calculations and precision.
The prediction framework has been integrated into the business interface of KPN, which marks the initial step in the automatization of short-term capacity planning. The research insights emphasize the intricate nature of accurate prediction of future demand and advocate for scalable solutions beyond building new capacity. These solutions range from short-term mitigation to long-term strategies designed to alleviate high network loads. They underscore the importance of the implementation and integration of
dynamic decision-making within a digital twin of the network to ensure sustained effectiveness.

An important tool in forensic science is the likelihood ratio (LR), which quantifies the strength of evidence. It does so by comparing the probabilities of the evidence under two mutually exclusive hypotheses, the prosecution hypothesis H_p and the defense hypothesis H_d. However, if the underlying probability model to determine these probabilities is not correct, this can lead to misleading conclusions, for example biases towards one of the hypotheses. The ability for an LR-system to produce LR-values that reflect the true probabilities of the evidence under the hypotheses is called `consistency'. Ensuring the consistency of LR-systems is necessary to prevent biases and inaccuracies.

Several methods to evaluate consistency of LR-systems have been developed over the past decade, but there has been a lack of thorough comparisons to identify which one is the most effective with real case data. In this thesis, the aim is to fill this gap by developing and optimizing the existing methods, and comparing them to one another. An in-depth comparative analysis will be conducted of various existing metrics, as well as some newly introduced metrics, to evaluate the consistency of LR-systems.

This study evaluates the consistency metrics C_llr^cal and devPAV. The individual metrics are optimized before comparing them to each other. A third metric is introduced, which is named Fid. This metric is based on advanced calibration techniques. It is compared to the previous two metrics to see which one performs best on different datasets. This performance is evaluated based on the metrics' abilities to distinguish between consistent and inconsistent LR-systems, their reliability in terms of their output and their sensitivity to dataset size. To measure this, several different datasets are used.

The results show that C_llr^cal outperforms the other metrics in distinguishing between consistent and inconsistent LR-systems. However, it falls short in terms of reliability, as it fails to assign the same values to different LR-systems that are all consistent. On the other hand, devPAV demonstrates high reliability, showing both reliability across different datasets and across different dataset sizes. The Fid metric shows similar performance to devPAV, but has the disadvantage of not working on smaller datasets. Therefore, as a metric it might not be preferred, although the method itself definitely shows interesting insights into the consistency of LR-systems.

These findings improve the tools we have for forensic evidence interpretation, helping to make forensic practices more accurate and reliable. By identifying the best metric for consistency, this research helps to make the criminal justice system fairer and more precise.

In many fields we are interested in inference for a complex stochastic process given limited observations regarding its state over time. This thesis therefore introduces an expectation propagation approach to backward filtering forward guiding for high-dimensional finite-state space models. The backward filtering forward guiding method is first derived for such models with a specific emphasis on the temporal dynamics, after which factorised guiding terms which exploit the inherent structure of the latent state space are introduced.

Performance of the method is assessed by comparing numerical results for statistical inference of a Susceptible-Infected-Recovered example problem. The expectation propagation approach performs comparably with existing methods in a particularly simple setting where state variables are observed individually, and performs very well in a more difficult setting which the familiar methods can not deal with. We conclude that a more advanced treatment of the approximate likelihood filtering phase may be warranted in such complex settings.

The research summarised in this work provides a first effort towards the development of more general expectation propagation based backward filtering procedures for other types of high-dimensional sequential data models. The work additionally elucidates connections between backward filtering with backward marginalisation and alternative approximate likelihood filtering procedures, suggesting multiple avenues for future research.

In this thesis, we evaluate the statistical procedure based on the similarity index proposed by Ypma and Ross in 'Determing the similarity between expected and observed ageing behavior'. The function for the similarity index is defined based on the inner product of two probability density functions, assumed to be related to the Weibull distribution. The evaluated statistical test aims to verify whether an observation of censored lifetime data is compliant with a given reference distribution. The test is compared to both the likelihood ratio test and a test using a variation of the similarity index. The comparison between these tests is based on their power function. First, a clear explanation of the complete statistical procedure using the similarity index is provided. Then the observations for which the test can be used are explained further. Its application and small limitations are shown using an example. Then, the two alternative tests are introduced. This will be followed by a theoretical overview of the power comparison method. Finally, the simulation for the power comparison is conducted. The power function is estimated for multiple relevant base cases along a few alternative parameter lines. It can then be concluded that the likelihood ratio test has consistently higher power than the similarity index test. However, the variation of the similarity index demonstrates a varying power, with instances of both higher and lower values than the original similarity index test.

been given to Human Activity Recognition (HAR) based on signals obtained by IMUs placed on different body parts. This thesis studies the usage of Deep Learning-based models to recognize different football activities in an accurate, robust, and fast manner. Several deep architectures were trained with data captured with IMU sensors placed on football players' bodies and their performances were compared. A combination of convolutional layers followed by recurrent (bidirectional) LSTM layers showed to achieve the best results with up to 96.71% of accuracy. When using normalized data via a calibration recording, these accuracies increased up to 98.2%. Results showed that deep learning models performed better in evaluation time and prediction accuracy than traditional machine learning algorithms. An end-to-end pipeline for football activity recognition was developed that can be extended to any other HAR task. With it, not only the training was explored, but also a sliding window evaluation procedure was proposed that can be used to efficiently analyze unseen IMU recordings and recognize the activities there present. This pipeline showed to be fast and robust especially with signals consistently calibrated and can be used to recognize movements on a real-time basis. It can be concluded that a combination of deep learning models and a sliding window evaluation procedure is suitable for fast and accurate HAR tasks and can be used as input for research on injury prevention. By training and evaluating the models with more data, ideally from uncontrolled experiments such as football matches, we expect to further improve the generalization property of the classifiers.

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.

In this thesis a model for interpolation of magnetic fields is constructed using Gaussian processes. This model takes the curl- and divergence-free properties of magnetic fields into account. The Gaussian process regression, or kriging, is tested on both simulated and real data. It is also attempted to reconstruct the magnetization of objects based on measurement data.

In baseball, pitchers have a high rate of throwing arm injury, which could lead to disability and less training time. This paper aims at investigating whether upcoming injuries of youth baseball pitchers can be detected before the athlete experiences injury symptoms. A total of 118 elite youth baseball pitchers from the Dutch national baseball team and six Dutch academies were followed over three years. Promising variables like Range of Motion, Muscle Force, Ball Speed and Training Time were included for use in a supervised classification problem. Prediction accuracy performance was then measured for different algorithms in the form of F1 and F2 scores. Results showed deficient performance for injury prediction using single-point-in-time measurements for all examined algorithms, with scores of both F1 and F2 reaching maximums of 0.5. The results, however, revealed the importance of measuring variables like hip force and hip range of motion for shoulder injury prediction, and force in the hip and shoulder together with the total rotational motion (TRM) of the shoulder for elbow injury prediction. Ball speed and training time contributed less for the tested models. Higher frequency data is needed for better injury prediction performance. Future studies are recommended to measure data with a time between measurements of one to two weeks. This high frequency makes it possible to use time-series analysis to detect slight asymptomatic pathology developments progressing over time, to help youth baseball pitchers avoid injuries and keep their performance ready for top-level play.

One interesting part of the application of human activity recognition is sports motion recognition and classification. In recent years, many commercial wearable devices have been used for recording and supervising motion data information during sports. However, their claimed high-accuracy results but motion recognition and classification method have not been proven. This thesis project presents work special related to tennis stroke detection and classification. An automated and comprehensive tennis stroke recognition and classification method based on the inertial measuring unit sensor (accelerometer and gyroscope) and machine learning algorithm (Support vector machines) was proposed in this study. Seven tennis players with a different level of tennis skills were tested and recorded using a self-made IMU sensor system with four sensors (forearm, upper arm, trunk, and pelvis). Video footage from Playsight was manually notated as the golden standard for stroke type identification. SVMs was constructed to train the classification model to classify true shots to eight types of tennis strokes from the IMU signals. Across leave-one-out seven-fold cross-validation, the SVMs classification models were trained with data from a single IMU sensor on the forearm and upper arm with the prediction accuracies of 0.69 and 0.70 respectively. And further, both SVMs models were trained by enlarged training data, resulting in improved prediction accuracies of 0.75 and 0.77. Noticeably, the best prediction accuracy was achieved by training the SVMs classification model with fused data from the previous two sensors and with the enlarged training data. The final prediction result was 0.79. Even though there exist deficiencies such as skill level different of subjects, insufficient training datasets which may lead the results of validation and prediction less credible, the IMU sensor and SVMs machine learning algorithm still played well in the tennis stroke classification task. And we expect to have better accuracy results by feeding enough training data and using data-fusion combination of different IMU sensors to the upper extremity to SVMs classification model in future work.

In this thesis we shall consider a generalization on Pólya Processes as have been described by Chung et al. [7]. Given finitely many bins, containing an initial configuration of balls, additional balls arrive one at a time. For each new ball, a new bin is created with probability 푝, or with probability 1 − 푝 this new ball shall be placed in an existing bin such that the probability of this ball ending in a specific bin, is proportional to 푓(푚) where 푚 is the number of balls currently in that bin and 푓 is some feedback function. We shall show that for 푝 = 0, which will be defined as Finite Pólya Processes, the behaviour of the process can be classified into one of three mutual exclusive regimes: Monopolistic Regime, Eventual Leadership Regime or Almost-Balanced Regime. This behaviour solely depends on the convergence of the following sums: Ση≥1 푓(푛)–1 and Ση≥1 푓(푛)-2. We shall explore the limiting distribution of fractions of balls in bins when 푓(푥) = 푥, which is a known result for classical multi-coloured Pólya Urn problems.Using a similar method, we find a limiting distribution for Finite Pólya Processes with general positive linear feedback functions, which has not previously been researched. We then consider the case where 푝 > 0, which are defined as Infinite Pólya Processes and restrict the feedback function to be of the form 푓(푥) = 푥γ where 훾 ∈ ℝ. We shall show that if 훾 > 1, almost surely one bin will dominate or a new bin will be created. We shall show that for 훾 = 1 a preferential attachment scheme arises. We consider 훾 < 1 under the assumptions that some limits exist and show that the fraction of bins having 푚 balls shrinks exponentially as a function of 푚. Finally, we reflect on our results and discuss interesting future research subjects.