Conflicting information and location parameter inference

摘要

The use of heavy-tailed distributions is a valuable tool in developing robust Bayesian procedures, limiting the influence of conflicting information on posterior inference. In this paper, the behavior of the posterior density of a location parameter is investigated when the sample contains outliers or the prior location is misspecified. Conditions on the tails of the prior and the likelihood are established to determine the proportion of conflicting information that can be rejected by the posterior. It is shown that the posterior distribution converges in law to a density proportional to the product of the densities of the non-conflicting information, as the outliers (and/or the prior location) go to plus or minus infinity, at any given rate. In particular, if the prior is non-conflicting, this limiting density is the posterior that would be obtained from the reduced sample, excluding the outliers. Examples are given to illustrate the results.