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Limiting posterior distributions under mixture of conjugate priors. (English) Zbl 0839.62012
Summary: Suppose the posterior distribution has a limiting distribution with respect to each member of a family of conjugate priors. Subject to a uniform boundedness condition on the prior parameters, the posterior distribution with respect to a mixture of member priors has the same limiting distribution. This result is used to show that a posterior distribution (given complete data) with respect to a mixture of Dirichlet processes priors can be approximated by a Brownian bridge. It also follows from this result that the limiting posterior distribution (given censored data) with respect to a mixture of beta-neutral processes priors is identical to the limiting sampling distribution of the Kaplan-Meier estimator.

62E20 Asymptotic distribution theory in statistics
62G20 Asymptotic properties of nonparametric inference
62C10 Bayesian problems; characterization of Bayes procedures
62G99 Nonparametric inference