Monte Carlo Approximation of Bayes Factors via Mixing With Surrogate Distributions

• Published in: Journal of the American Statistical Association Vol. 117; no. 538; pp. 765 - 780
• Main Authors: Dai, Chenguang, Liu, Jun S.
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 03.04.2022; Taylor & Francis Ltd
• Subjects: Algorithms; Approximation; Bayesian analysis; Bayesian theory; Convergence; Gaussian process; Jumping; Marginal likelihood; Markov analysis; Markov chain; Markov chains; Mathematical analysis; Mixture distribution; momentum; Monte Carlo simulation; Multiple-try Metropolis; Normalizing (statistics); Regression analysis; Reversible; Reversible jump MCMC; Statistical analysis; Statistical methods; Statistical models; Statistics; Wang-Landau algorithm
• ISSN: 0162-1459; 1537-274X; 1537-274X
• DOI: 10.1080/01621459.2020.1811100

By mixing the target posterior distribution with a surrogate distribution, of which the normalizing constant is tractable, we propose a method for estimating the marginal likelihood using the Wang-Landau algorithm. We show that a faster convergence of the proposed method can be achieved via the momentum acceleration. Two implementation strategies are detailed: (i) facilitating global jumps between the posterior and surrogate distributions via the multiple-try Metropolis (MTM); (ii) constructing the surrogate via the variational approximation. When a surrogate is difficult to come by, we describe a new jumping mechanism for general reversible jump Markov chain Monte Carlo algorithms, which combines the MTM and a directional sampling algorithm. We illustrate the proposed methods on several statistical models, including the log-Gaussian Cox process, the Bayesian Lasso, the logistic regression, and the g-prior Bayesian variable selection. Supplementary materials for this article are available online.