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A Large Deviations Principle for Dirichlet Process Posteriors
Ganesh, A.J.; O'Connell, Neil
HPLBRIMS9805
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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