Assessing Sensitivity to Priors Using Higher Order Approximations

Higher order likelihood methods lead to an easily implemented and highly accurate approximation to both joint and marginal posterior distributions. This makes it quite straightforward to assess the influence of the prior, and to assess the effect of changing priors, on the posterior quantiles. We discuss this in the light of some simple examples that illustrate in concrete form the potential for marginal posterior densities from seemingly uninformative priors to be poorly calibrated.