Abstract: 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 prior 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 prior is identical to the limiting sampling distribution of the Kaplan-Meier estimator.
Key words and phrases: Mixtures of conjugate priors, mixtures of beta neutral processes priors, mixtures of Dirichlet processes priors, mixtures of weighted gamma processes priors, limiting posterior distributions.