Monte Carlo Approximation of Bayes Factors via Mixing With Surrogate Distributions

Chenguang Dai and Jun S. Liu

Journal of the American Statistical Association, 2022, vol. 117, issue 538, 765-780

Abstract: 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.

Date: 2022
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DOI: 10.1080/01621459.2020.1811100

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