ON BARTLETT ADJUSTMENTS FOR APPROXIMATE BAYESIAN-INFERENCE

In wide generality, the posterior distributions of the likelihood rati o statistic and the posterior ratio statistic are chi-squared to error of order O(n(-1)), where n is sample size. The error in the chi-squar ed approximation can be reduced to order O(n(-2)) by Bartlett correcti on. In this paper, explicit formulae are derived for the Bartlett adju stment factors of both statistics, and the derivations are based on th e Tierney, Kass & Kadane (1989) asymptotic approximation for marginal posterior probability density functions. The use of numerical differen tiation to facilitate calculation of the Bartlett adjustments is also described. Some applications are considered that concern inference abo ut regression models from both complete and right-censored data.