THE LAPLACIAN T-APPROXIMATION IN BAYESIAN-INFERENCE

A remarkably accurate approximation is proposed for a marginal density, for finite sample situations where the tails of the posterior density are not accurately represented by a more standard Laplacian approximation. An approximation is developed for the posterior density of an arbitrary linear combination of the means, in the context of the Bayesian analysis of the multi-parameter Fisher-Behrens problem. Advantages of Laplacian methods for non-linear regression problems, when compared with sampling based methods, are discussed.