A note on marginal posterior simulation via higher-order tail area approximations

TL;DR

This paper introduces a higher-order tail area approximation method for Bayesian simulation, offering an efficient alternative to MCMC that produces independent samples with reduced computational effort.

Contribution

It presents a novel approximation-based simulation scheme for marginal posterior distributions that is simpler and faster than traditional MCMC methods.

Findings

Samples are drawn independently, reducing correlation.

Lower computational time compared to MCMC.

Applicable to diverse models like genetic linkage and logistic regression.

Abstract

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.