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Circular Data Modelling

Bachelor’s and Master’s Theses

2016-2017

Bayesian estimation for circular data: The wrapping approach

Research for this project will be conducted by Inge Jansen for her masters’ thesis for the Methodology and Statistics research master. It will focus on 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 will be developed.  The performance, efficiency, flexibility and ease of interpretation of these two methods will be investigated and compared to the other approaches.

 

2015-2016

Fitting mixtures of von Mises components with a reversible jump MCMC sampler

Research for this project will be 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 will be developed and applied to a real world sample of listening behavior data. The clusters created from the behavioral patterns will be 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.

 

2014-2015

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 at the Methodology and Statistics section). 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.

Ba thesis Jolien Ketelaar

 

2013-2014

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.

MSc thesis Jolien Cremers

 

Extending Bayesian analysis of circular data to comparison of multiple groups

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.

An understandable summary of the thesis can be found here.

The full thesis can be found here.

Code for the study can be found on this GitHub page.