Let Xk be a sequence of independent and identically distributed random variables taking values in a compact metric space O, and consider the problem of estimating the law of K1 in a Bayesian framework. A conjugate family of priors for non-parametric Bayesian inference is 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 predictive probability of ruin in the classical gambler's ruin problem.

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In: Bernoulli

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