Mixtures of Bivariate von Mises Distributions with Applications to Modelling of Protein Dihedral Angles

The modelling of empirically observed data is commonly done using mixtures of probability distributions. In order to model angular data, directional probability distributions such as the bivariate von Mises (BVM) is typically used. The critical task involved in mixture modelling is to determine the optimal number of component probability distributions. We employ the Bayesian information-theoretic principle of minimum message length (MML) to distinguish mixture models by balancing the trade-off between the model's complexity and its goodness-of-fit to the data. We consider the problem of modelling angular data resulting from the spatial arrangement of protein structures using BVM distributions. The main contributions of the paper include the development of the mixture modelling apparatus along with the MML estimation of the parameters of the BVM distribution. We demonstrate that statistical inference using the MML framework supersedes the traditional methods and offers a mechanism to objectively determine models that are of practical significance.