When: Friday, 27 July 2012 3:00 PM-4:00 PM (GMT+10:00) Brisbane.
Where: O314, QUT Gardens Point campus
PhD Confirmation of Candidature Seminar – Miss Zoé van Havre
Title: Asymptotic and large sample properties of over-fitted Bayesian mixture models
Principal Supervisor: Professor Kerrie Mengersen
Non-QUT Supervisor: Professor Judith Rousseau
Associate Supervisor: Dr. Nicole White
Chair of the Panel – Prof. Kerrie Mengersen
Dr. Nicole White
Dr Adrian Barnett
External Prof. Judith Rousseau
Mixture models are a rich class of statistical methods which can be applied to almost any problem, and lend themselves particularly well to the analysis of today’s complex, high-dimensional datasets. Mixtures occur when observations can be assumed to have come from one of a number of different populations; in such cases a single parametric model is not adequate to model the variation in the response. The number of underlying populations and their parameters are usually unknown and of much interest.
Estimating the number of components in a mixture has been an area of contention for over 100 years, and to this day while many exist and continue to be published, no single method has yet to adequately solve this problem (Fruhwirth-Schnatter 2006, McLachlan & Peel 2000). This is in large part due to non-identifiability which affects all mixtures when the number of components is overfitted. Occurring when more components are included in the model than are present in the underlying population, this is an implicit part of all existing methods, whether they compare various models or sample the multidimensional space encompassing a group of models. Recently, Rousseau & Mengersen (2011) proved that the asymptotic behaviour of the estimated distribution of the parameters in over-fitted mixture models depends on the prior on the mixture weights, and given some restrictions this behaviour has stable and interesting behaviour. This result is very significant, and the purpose of this thesis is to extend the theory and apply this discovery to a wider range of models and applications. If successful, this work will provide a statistically sound alternative to the methods currently needed to estimate the true number of components in a mixture.