  The modelling of data on a spherical surface requires the consideration of
directional probability distributions. To model asymmetrically distributed data
on a three-dimensional sphere, Kent distributions are often used. The moment
estimates of the parameters are typically used in modelling tasks involving
Kent distributions. However, these lack a rigorous statistical treatment. The
focus of the paper is to introduce a Bayesian estimation of the parameters of
the Kent distribution which has not been carried out in the literature, partly
because of its complex mathematical form. We employ the Bayesian
information-theoretic paradigm of Minimum Message Length (MML) to bridge this
gap and derive reliable estimators. The inferred parameters are subsequently
used in mixture modelling of Kent distributions. The problem of inferring the
suitable number of mixture components is also addressed using the MML
criterion. We demonstrate the superior performance of the derived MML-based
parameter estimates against the traditional estimators. We apply the MML
principle to infer mixtures of Kent distributions to model empirical data
corresponding to protein conformations. We demonstrate the effectiveness of
Kent models to act as improved descriptors of protein structural data as
compared to commonly used von Mises-Fisher distributions.
