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.

摘要

通过将目标后验分布与代理分布混合，其中归一化常数易于处理，我们提出了一种使用 Wang-Landau 算法估计边际似然的方法。我们表明，通过动量加速可以实现所提出方法的更快收敛。详细介绍了两种实施策略：（i）通过多次尝试 Metropolis（MTM）促进后验分布和代理分布之间的全局跳跃；(ii) 通过变分近似构造代理。当一个代理难以获得时，我们描述了一种新的通用可逆跳跃马尔可夫链蒙特卡罗算法的跳跃机制，它结合了 MTM 和定向采样算法。我们在几个统计模型上说明了所提出的方法，包括对数高斯 Cox 过程，贝叶斯套索、逻辑回归和 g-先验贝叶斯变量选择。本文的补充材料可在线获取。