A multivariate von Mises distribution with applications to bioinformatics

Kanti V. Mardia, Gareth Hughes, Charles C. Taylor, & Harshinder Singh

Motivated by problems of modeling torsional angles in molecules, Singh et al. (2002) proposed a bivariate circular model which is a natural torus analogue of the bivariate normal distribution and a natural extension of the univariate von Mises distribution to the bivariate case. In this paper, we propose a multivariate extension of the bivariate model of Singh et al. The results about conditional distributions are derived and the shapes of marginal distributions have been investigated for a special case. Procedures for the estimation of parameters of the proposed distribution include the method of moments, and pseudolikelihood; the efficiency of the latter is investigated in two and three dimensions. The methods are applied to real protein data of conformational angles.

Keywords: Bias; Bessel functions; Circular mean; Circular variance; Gamma turns; Proteomics; Pseudolikelihood.