Tibbits Matthew M, Groendyke Chris, Haran Murali, Liechty John C
Department of Statistics, Pennsylvania State University.
Department of Mathematics, Robert Morris University.
J Comput Graph Stat. 2014;23(2):543-563. doi: 10.1080/10618600.2013.791193.
Markov chain Monte Carlo (MCMC) algorithms offer a very general approach for sampling from arbitrary distributions. However, designing and tuning MCMC algorithms for each new distribution, can be challenging and time consuming. It is particularly difficult to create an efficient sampler when there is strong dependence among the variables in a multivariate distribution. We describe a two-pronged approach for constructing efficient, automated MCMC algorithms: (1) we propose the "factor slice sampler", a generalization of the univariate slice sampler where we treat the selection of a coordinate basis (factors) as an additional tuning parameter, and (2) we develop an approach for automatically selecting tuning parameters in order to construct an efficient factor slice sampler. In addition to automating the factor slice sampler, our tuning approach also applies to the standard univariate slice samplers. We demonstrate the efficiency and general applicability of our automated MCMC algorithm with a number of illustrative examples.
马尔可夫链蒙特卡罗（MCMC）算法提供了一种从任意分布中进行采样的非常通用的方法。然而，为每个新分布设计和调整MCMC算法可能具有挑战性且耗时。当多元分布中的变量之间存在强相关性时，创建一个高效的采样器尤其困难。我们描述了一种构建高效、自动化MCMC算法的双管齐下的方法：（1）我们提出了“因子切片采样器”，它是单变量切片采样器的推广，我们将坐标基（因子）的选择视为一个额外的调整参数；（2）我们开发了一种自动选择调整参数的方法，以构建一个高效的因子切片采样器。除了使因子切片采样器自动化外，我们的调整方法也适用于标准的单变量切片采样器。我们通过一些示例展示了我们的自动化MCMC算法的效率和普遍适用性。
