B1097
Title: Bayesian inference and model selection in directional statistics
Authors: Christopher Fallaize - University of Nottingham (United Kingdom) [presenting]
Abstract: The likelihood functions of many distributions used to model directional data, such as Bingham and matrix-Fisher distributions, contain normalising constants which are somewhat awkward to work with. This complicates Bayesian inference, since these constants depend on the parameter of interest, and hence are required when using traditional simulation-based techniques such as the basic forms of Markov chain Monte Carlo (MCMC) samplers. Such problems are termed doubly-intractable, since both the normalising constant of the likelihood as well as the marginal likelihood of the data are intractable. One possible strategy is to use an approximation to the normalising constant and then perform a standard analysis using MCMC. Here we show how, using recent advances in MCMC methodology for doubly-intractable problems, it is possible to perform exact (Monte Carlo) inference for the unknown parameters, in the sense that samples are drawn from the exact posterior distribution of the parameter of interest. The problem of choosing between competing models will also be discussed, where the use of traditional methods (such as Bayes factors) is again complicated by the presence of the awkward normalising constant. The methods will be illustrated on real data from applications in directional statistics.
Journal