Bachelor’s and Master’s Theses
Bayesian estimation for circular data: The wrapping approach
Research for this project was conducted by Inge Jansen for her masters’ thesis for the Methodology and Statistics research master. The subject of this thesis was the wrapping approach to circular data, in which a distribution on the real line is ‘wrapped’ around the circle. In prior work (Master Theses 2013/2014) an embedding approach, using the projected normal distribution, for regression models and an intrinsic approach using the Von Mises distribution for analysis of variance models were investigated. For both types of models (ANOVA and regression), Markov Chain Monte Carlo (MCMC) methods using the wrapping approach were developed. Furthermore, the performance, efficiency, flexibility and ease of interpretation of these two methods were investigated and compared to the other approaches.
Fitting mixtures of von Mises components with a reversible jump MCMC sampler
Research for this project was conducted by Pieter Jongsma for his Masters’ thesis for the Methodology and Statistics research master. Bayesian methods for the analysis of mixture models for analysing data in a circular context were developed and applied to a real world sample of listening behavior data. The clusters created from the behavioral patterns were compared on music genre preference, frequency of use, user retention or other attributes of interest to the creators of the music service. The thesis has since been submitted for publication.
It is all about the circle: An inventory of circular data
Research for this project was done by Jolien Ketelaar for her bachelor’s thesis for the Educational Sciences bachelor programme (thesis written under the Methodology and Statistics department). In this study it was investigated how circular data are described and analyzed by reviewing 17 research articles. In addition, 8 data sets were (re)analyzed to further investigate some of the characteristics of empirical circular data.
Assessing a Bayesian embedding approach to circular regression models
Research for this project was done by Jolien Cremers and served as her masters’ thesis for the Methodology and Statistics research master. It focused on assessing a Bayesian embedding approach to circular regression models in terms of performance, efficiency and flexibility using several simulation studies. It was found that the method performs reasonably well (in terms of bias and coverage). Additional research, after completion of the masters’ thesis, has shown that using a slightly different MCMC sampling scheme will result in even better performance and a far greater computational efficiency. However, the most promising aspect of the method that was assessed is its flexibility of use for applied researchers. Using this method they will be able to analyze regression models with a circular outcome and several types of predictor variables.
The Master Thesis of Kees Mulder focused on the extension of Bayesian circular data models to between-subjects (i.e. ANOVA-like) contexts. Three MCMC-methods were developed, and compared to one another, of which one was found to be most promising.
This thesis was one of three nominees for the Utrecht University Best Graduate Thesis Award 2014-2015.