On the variability of case-deletion importance sampling weights in the Bayesian linear model

A standard specification of the Bayesian linear model is presented. The required and sufficient conditions for the variance of the case-deletion importance sampling weights to be finite are derived. The conditions rely on simple relationships concerning the scale parameter of the prior distribution of the error variance and familiar frequentist quantities. The conditions are easy to check, therefore providing a quick and effective method for deciding whether or not crude importance sampling will generate reliable estimates of functionals with respect to the case-deletion posterior.
1. INTRODUCTION Importance sampling techniques can be used to reweight a sample from some distribution to estimate functionals with respect to a different distribution. This approach has found routine application [...]