Improved marginal likelihood estimation via power posteriors and importance sampling

• Main Authors: LI, Yong, WANG, Nianling, Jun YU
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2019
• Subjects: Bayes factor; Marginal likelihood; Markov Chain Monte Carlo; Model choice; Power posteriors; Importance sampling; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/2287; https://ink.library.smu.edu.sg/context/soe_research/article/3286/viewcontent/PB29_.pdf
• Institution: Singapore Management University

The power-posterior method of Friel and Pettitt (2008) has been used to estimate the marginal likelihoods of competing Bayesian models. In this paper it is shown that the Bernstein-von Mises (BvM) theorem holds for the power posteriors under regularity conditions. Due to the BvM theorem, the power posteriors, when adjusted by the square root of the corresponding grid points, converge to the same normal distribution as the original posterior distribution, facilitating the implementation of importance sampling for the purpose of estimating the marginal likelihood. Unlike the power-posterior method that requires repeated posterior sampling from the power posteriors, the new method only requires the posterior output from the original posterior. Hence, it is computationally more efficient to implement. Moreover, it completely avoids the coding efforts associated with drawing samples from the power posteriors. Numerical efficiency of the proposed method is illustrated using two models in economics and finance.