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

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.

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.

In today’s complex, modern world, where more data and knowledge is available then ever before, consensus over approaches in statistics is far away. To understand what this means for forensic statistics, both the frequentist and Bayesian approach are considered in quantifying evidence. Classical frequentist approaches are elaborated according to an example of knife data, where both univariate and multivariate approaches are applied. As an alternative to the previous methods, the likelihood ratio is introduced. To arrive at a unified framework for calculating likelihood ratios, the European Union funded a project to calculate likelihood ratios using a software package with a user friendly interface called SAILR. Calculating the likelihood ratio is mostly done by using feature based models. A feature based model used by SAILR will be elaborated according to a glass comparison example. When the feature based model is illustrated, an extension on the model will be given using a non-parametric function. The discussed models will be elaborated and applied on test data from and international drugs comparison project using SAILR. As an alternative to feature based models, a score based model is introduced and compared to the previous drugs comparison results of the feature based model.

Model selection starts with a dataset and a number of candidate models that can explain that data. The AIC
and BIC criteria prevents choosing the best fitting model by penalizing for the number of parameters in a
model and instead selects the model that performs best when assessed to unseen data. Their performance
depends on the sample size and the noise in the data.
In portfolio management, it is common to find a combination of financial products such that an objective
is optimized. A common risk measure criterion that gets maximized is the Sharpe ratio. Since portfolio management
is also done based on historic data, but wanted to be optimized for unseen data, model selection
can be applied to portfolio management as well.
Finding the optimal weights in a portfolio is done by solving a linear system of equations. Applying this
to subsets of stocks which are contained in the AEX index, leads to higher in-sample Sharpe ratios than using
equal weights or just following the AEX index. The out-of-sample Sharpe ratio gets overestimated by noise
fit and estimation error. The Sharpe Ratio Information Criterion (SRIC) corrects for this. This criterion gives
an unbiased estimate for the out-of-sample Sharpe ratio and can be used for model selection in portfolio
management. Using a trend following strategy, investing proportionally to the returns, also increases your
expected out-of-sample Sharpe ratio.

When the re brigade arrives at a burning building, it is of vital importance that people who are still inside can quickly be found. In this thesis we contribute to an ultrasonic sound sensor for human presence detection in smoke-lled spaces. This type of sensor could assist the re brigade when evacuating a large building by directing them to the places where their help is most needed. The advantage of ultrasonic sound over other sensors or cameras is that its signal is able to pierce through smoke, does not require badges or other wearable devices and introduces little privacy and security risks. In addition, ultrasonic sensors are very inexpensive making it possible to equip every room of a building with an ultrasonic presence detector. In this research an ultrasonic sensor was built for less than 20 Euros and it was found to be unaected by the glycerine based smoke that it was tested in. Using a particle filter based on sequential importance resampling as well as a Filter based on Gaussian approximation of the posterior density the resulting system was reliably able to detect when there was a single person walking in the sensor direction, even when other sources of movement such as doors and chairs were present.

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.

Background: One of the biggest challenges of analyzing electroencephalogram (EEG) data in pain processing is the low signal-to-noise ratio (SNR). A common method to increase the SNR is to average time-locked responses over repeated trials. Unfortunately, relevant information is lost due to averaging. In addition, EEG responses are influenced by psychophysical elements, such as stimulus intensity and stimulus detection. Therefore, to reduce the loss of information and to control for psychophysical elements we developed a novel analysis method using linear mixed-effect (LME) models. Furthermore, capsaicin was used to challenge the novel method with the goal to quantify peripheral and central sensitization effects.

New method: LME models were used to include all EEG trials into one model to reduce the loss of information caused by averaging. In addition, phase locked and non-phase locked EEG data were combined with psychophysical data to control for psychophysical elements.

Results: Including all EEG trials into one model made it possible to perform statistical analyses. Moreover, combining EEG data with psychophysical data showed effects of stimulus detection, stimulus amplitude and the number of pulses on EEG responses. Although the LME models were able to test for significant effects after capsaicin application, the analyses did not show sensitization effects.

Comparison with existing methods: The phase locked EEG data was analyzed using conventional time-domain averaging methods and compared with LME models which included all EEG trials into one model.

Conclusion: This study showed that the novel LME method could be used to perform statistical analyses using all EEG trials and detect significant differences over time. In addition, psychophysical elements such as stimulus detection, amplitude and number of pulses could be controlled for both phase locked and non-phase locked EEG analyses. Probably, attention and learning effects played a role in the interpretation of the effects of capsaicin. Although application of this novel method showed no peripheral and central sensitization effects induced by capsaicin, it did show the potential of LME models in phase locked and non-phase locked EEG analyses.

ASML produces TwinScan NXT machines that are used for the production of microchips. The machines ensure that an accurate pattern of DUV-light passes a lens and that it is projected as accurate as possible on the wafer. To ensure that the focal point of the converged DUV-light falls exactly onto the wafer, the leveling functionality is of great importance. That is, placing the wafer in the correct depth of focus by rotating the wafer and moving the wafer up or down during exposure.
In order to meet the imaging requirements, the performance is investigated by analyzing errors of the machines at customers' site, considering one-year data. The most important errors are A, B, C and D. To reduce the total unscheduled down (USD) time of those errors, we should focus on reducing the mean USD time for errors A and C; and focus on reducing the frequency for errors B andD where these last two errors are likely to be solved together.
Different nominal customer-related variables are considered as possible causes of USD times such as location, system type or type of sensors. After applying hierarchical clustering and multidimensional scaling, the variable set is reduced. This set is used to model the USD time of one error: B. Significant differences in USD times are found, showed by the robust and distribution free rank tests: Wilcoxon and Kruskal-Wallis test.
To discover interesting patterns among variables, regression models are applied. The linear regression model and generalized linear model not seem to be the right model to the data. The zero adjusted exponential model seems to be the correct model and show that AG type, location and FSM flex package are the most important explanatory variables. This directs to a potential root cause where ASML is working further upon.