Approximate marginal densities of independent parameters

Abstract

This paper presents an asymptotic approximation for the marginal density of any parameter of interest of a joint posterior density in the case of independent parameters. The approximation is based on the signed-root-based importance sampling algorithm considered in Kharroubi and Sweeting [Posterior simulation via signed root log-likelihood ratios, Bayesian Anal. (2010), in press] and gives rise to the alternative simulation-consistent scheme to Markov chain Monte Carlo for marginal densities. The consideration is illustrated by a censored regression model.

Keywords:

• Bayesian inference
• importance sampling
• signed root log-likelihood ratio
• simulation