Bayesian analysis for bivariate von Mises distributions

There has been renewed interest in the directional Bayesian analysis for the bivariate case especially in view of its fundamental new and challenging applications to bioinformatics. The previous work had concentrated on Bayesian analysis for univariate von Mises distribution. Here, we give the description of the general bivariate von Mises (BVM) distribution and its properties. There are various submodels of this distribution which have become important and we give a review of these submodels. Also, we derive the normalizing constant for the general BVM distribution in a compact way. Conjugate priors and posteriors for the general case and the submodels are obtained. The conjugate prior for a multivariate von Mises distribution is also examined.