Identification of Regeneration Times in MCMC Simulation, With Application to Adaptive Schemes
Identification of Regeneration Times in MCMC Simulation, With Application to Adaptive Schemes
复制标题
MCMC 仿真中再生时间的识别及其在自适应方案中的应用
DOI：
10.1198/106186005x47453
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发表时间：
2005
影响因子：
2.4
通讯作者：
J. Kadane
中科院分区：
文献类型：
--
作者：
A. Brockwell;J. Kadane
在马尔可夫链蒙特卡罗模拟中，再生是一个有用的工具，因为它可以用来避开老化问题，并对参数估计本身的方差构造更好的估计。它还提供了一种简单的方法来将自适应行为引入马尔可夫链，并使用并行处理器来构建单链。再生往往很难利用，因为对于大多数链来说，不存在循环的适当原子，而且使用Nummelin的分裂方法来确定再生时间并不总是容易的。本文描述了一种构造具有指定目标分布的马尔可夫链和识别再生时间的方法。作为该方法的一个特例，给出了一个可以“包裹”在现有马尔可夫转移核上的算法。此外，还介绍了一种在再生时自适应过渡核的具体规则，该规则使用与目标密度的混合法线近似作为其建议密度，逐步用独立采样的Metropolis-Hastings核来代替原始的过渡核。通过算例说明了再生自适应算法的计算优势。
Regeneration is a useful tool in Markov chain Monte Carlo simulation because it can be used to side-step the burn-in problem and to construct better estimates of the variance of parameter estimates themselves. It also provides a simple way to introduce adaptive behavior into a Markov chain, and to use parallel processors to build a single chain. Regeneration is often difficult to take advantage of because, for most chains, no recurrent proper atom exists, and it is not always easy to use Nummelin's splitting method to identify regeneration times. This article describes a constructive method for generating a Markov chain with a specified target distribution and identifying regeneration times. As a special case of the method, an algorithm which can be “wrapped” around an existing Markov transition kernel is given. In addition, a specific rule for adapting the transition kernel at regeneration times is introduced, which gradually replaces the original transition kernel with an independence-sampling Metropolis-Hastings kernel using a mixture normal approximation to the target density as its proposal density. Computational gains for the regenerative adaptive algorithm are demonstrated in examples.