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A Large Deviations Principle for Dirichlet Process Posteriors

Ganesh, A.J.; O'Connell, Neil

HPL-BRIMS-98-05

Keyword(s): large deviations; Bayesian statistics; Dirichlet process

Abstract: Let X(sub k) be a sequence of iid random variables taking values in a compact metric space omega, and consider the problem of estimating the law of X(sub 1) in a Bayesian framework. A conjugate family of priors for non- parametric Bayesian inference are the Dirichlet process priors popularized by Ferguson. We prove that if the prior distribution is Dirichlet, then the sequence of posterior distributions satisfies a large deviation principle, and give an explicit expression for the rate function.

16 Pages

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