Mixtures of concentrated multivariate sine distributions with applications to bioinformatics

Abstract

Motivated by examples in protein bioinformatics, we study a mixture model of multivariate angular distributions. The distribution treated here (multivariate sine distribution) is a multivariate extension of the well-known von Mises distribution on the circle. The density of the sine distribution has an intractable normalizing constant and here we propose to replace it in the concentrated case by a simple approximation. We study the EM algorithm for this distribution and apply it to a practical example from protein bioinformatics.

Keywords:

• approximate MLEs
• directional statistics
• EM algorithm
• mixture model
• protein structure
• von Mises distribution

Acknowledgements

We thank Wouter Boomsma and Jes Frellsen for their protein data set and useful discussions. The work of Zhengzheng Zhang was funded by a Dorothy Hodgkin postgraduate award co-sponsored between BBSRC and GlaxoSmithKline. This paper was improved substantially following helpful comments by the referees.