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R.V. Ramamoorthi
Department of Statistics and Probability Michigan State University
Consistency of posterior distributions
Monday, May 19, 20084:00 PM
Engineering 2 Building, room 599
Abstract:
The advent of powerful computing resources has lead to a surge in the development and use of Bayesian methods. The Bayesian method begins with a prior distribution which is then updated to the posterior distribution using data. The sequence of posterior is consistent at a parameter value "theta" if, when "theta" is ``true'' then for observations on a set of probability 1, the sequence of posterior converges to the point mass at "theta".
Consistency of posterior distribution presents an initial theoretical framework to assess the behaviour of the Bayesian model and is a kind of frequentist validation of the Bayesian method. This talk will give an overview of some of the theoretical issues related to consistency for priors on densities. We will discuss some methods useful in establishing consistency and application of these methods in the context of some popular models.