Marginal posterior simulation via higher-order tail area approximations

In this paper we explore the use of higherorder tail area approximations for Bayesian simulation. These approximations give rise to alternative simulation schemes to MCMC for Bayesian computation of marginal posterior distributions for a scalar parameter of interest, in the presence of nuisance parameters. Their advantage over MCMC methods is that samples are drawn independently and much lower computational time is needed. The methods are illustrated by a genetic linkage model, a normal regression with censored data and a logistic regression model.