  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.
