Title
Aspects of Bayesian Inference by Posterior Simulation for some Latent Structure Models
Speaker
Ernest Parfait Fokoue, University of Glasgow, United Kingdom
Abstract
Whether one chooses to view it as a Finite Mixture of Multivariate Gaussians with structured covariance matrices, or as a Factor Analytic model in heteregeneous input space, the Mixture of Factor Analysers model that I will focus on in this talk is a potentially very useful latent structure model that has come under quite close scrutiny in recent years. I will briefly introduce the model, and I will then justify and motivate the need for a Bayesian solution based on posterior simulation as a good alternative to the likelihood based treatment via the EM algorithm and the Bayesian inference solution via Variational Approximation studied by Ghahramani and Beal(2000). I will more precisely present elements of the construction of ergodic Markov chains for both the estimation of model parameters and the determination of model complexity through Data Augmentation and the simulation of a continuous-time birth-and-death point process, drawing on ideas and results from Diebolt and Robert (1994), Richardson and Green (1997), Lopes and West (2000), Fokoue and Titterington (2000), Celeux (1998), Stephens (1997, 2000) and Hurn and al. (2000).
