MSc in Statistical Science, Oxford University
Double licence M.I.A.S.H.S, Université Paris 1 Panthéon-Sorbonne & SciencesPo Paris
Foundations and applications in Bayesian Mixture Modelling.
Mixtures are a popular class of models bridging parametric and non-parametric statistics and, as part of the standard data analysis toolkit, have ubiquitous applications in regression, clustering, machine learning, etc. One of the main goals of this thesis is to ease model selection within such a class of models, in particular by finding efficient ways of computing the marginal likelihood (aka evidence) of semi-parametric models (such as Dirichlet Process Mixtures). We also study the convergence properties of the Bayes Factor when comparing such parametric and semi-parametric models.