We explore the use of higher-order tail area approximations for Bayesian
simulation. These approximations give rise to an alternative simulation scheme
to MCMC for Bayesian computation of marginal posterior distributions for a
scalar parameter of interest, in the presence of nuisance parameters. Its
advantage over MCMC methods is that samples are drawn independently with lower
computational time and the implementation requires only standard maximum
likelihood routines. The method is illustrated by a genetic linkage model, a
normal regression with censored data and a logistic regression model
