ON THE EFFICACY OF BAYESIAN-INFERENCE FOR NONIDENTIFIABLE MODELS

Although classical statistical methods are inapplicable in point estim ation problems involving nonidentifiable parameters, a Bayesian analys is using proper priors can produce a closed form, interpretable point estimate in such problems. The question of whether, and when, the Baye sian approach produces worthwhile answers is investigated. In contrast to the preposterior analysis of this question offered by Kadane, we e xamine the question conditionally, given the information provided by t he experiment. An important initial insight on the matter is that post erior estimates of a nonidentifiable parameter can actually be inferio r to the prior (no-data) estimate of that parameter, even as the sampl e size grows to infinity. In general, our goal is to characterize, wit hin the space of prior distributions, classes of priors that lead to p osterior estimates that are superior, in some reasonable sense, to one 's prior estimate. This goal is shown to be feasible through a detaile d examination of a particular two-parameter Binomial model. Our result s support the proposition that a Bayesian analysis tends to be efficac ious in the estimation problem studied, and suggest that Bayesian upda ting can produce useful answers in the presence of nonidentifiability.