Publication Type
Working Paper
Version
publishedVersion
Publication Date
7-2019
Abstract
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.
Keywords
Bayes factor, Marginal likelihood, Markov Chain Monte Carlo, Model choice, Power posteriors, Importance sampling
Discipline
Econometrics
Research Areas
Econometrics
First Page
1
Last Page
37
Publisher
SMU Economics and Statistics Working Paper Series, Paper No. 16-2019
City or Country
Singapore
Citation
LI, Yong; WANG, Nianling; and Jun YU.
Improved marginal likelihood estimation via power posteriors and importance sampling. (2019). 1-37.
Available at: https://ink.library.smu.edu.sg/soe_research/2287
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.