A new method for posterior simulation is proposed, based on the combination of higher-order asymptotic results with the inverse transform sampler. This method can be used to approximate marginal posterior distributions, and related quantities, for a scalar parameter of interest, even in the presence of nuisance parameters. Compared to standard Markov chain Monte Carlo methods, its main advantages are that it gives independent samples at a negligible computational cost, and it allows prior sensitivity analyses under the same Monte Carlo variation. The method is illustrated by a genetic linkage model, a normal regression with censored data and a logistic regression model.
"Marginal Posterior Simulation via Higher-order Tail Area Approximations." Bayesian Anal. 9 (1) 129 - 146, March 2014. https://doi.org/10.1214/13-BA851