Some Fundamental Properties of a Multivariate von Mises Distribution

TL;DR

This paper investigates the conditions under which a multivariate von Mises distribution is unimodal, providing criteria for unimodality, examples of multimodal cases, and a sampling method for high concentration scenarios.

Contribution

It offers the first comprehensive criteria for unimodality of the multivariate von Mises distribution and introduces a sampling technique for high concentration cases.

Findings

Provided sufficient criteria for unimodality.

Showed examples of multimodal distributions.

Proposed a sampling method for high concentration.

Abstract

In application areas like bioinformatics multivariate distributions on angles are encountered which show significant clustering. One approach to statistical modelling of such situations is to use mixtures of unimodal distributions. In the literature (Mardia et al., 2011), the multivariate von Mises distribution, also known as the multivariate sine distribution, has been suggested for components of such models, but work in the area has been hampered by the fact that no good criteria for the von Mises distribution to be unimodal were available. In this article we study the question about when a multivariate von Mises distribution is unimodal. We give sufficient criteria for this to be the case and show examples of distributions with multiple modes when these criteria are violated. In addition, we propose a method to generate samples from the von Mises distribution in the case of high concentration.