标题： 基于群体的可逆跳马尔可夫链蒙特卡洛 显示英文标题

标题： Population-Based Reversible Jump Markov Chain Monte Carlo

摘要： 本文提出了一种基于群体的马尔可夫链蒙特卡洛（MCMC）方法在跨维情形下的扩展。基于MCMC推断的主要挑战之一是从高维和跨维目标测度中进行模拟。在这种情况下，MCMC方法可能无法充分遍历目标分布的支持区域；由此得到的模拟结果将是不可靠的。我们开发了群体方法来解决此类问题，并在适度假设下证明了这些群体算法的一致遍历性。这一结果被用来展示，在贝叶斯变量选择问题中，群体转移核相对于可逆跳跃采样器在收敛速度方面的优越性。此外，我们还给出了一个用于具有未知分量数量的贝叶斯多元混合模型的群体算法示例。该算法应用于六个维度上1000个数据点的基因表达数据，并证明我们的算法在性能上优于某些竞争性的马尔可夫链采样器。 显示英文摘要

摘要： In this paper we present an extension of population-based Markov chain Monte Carlo (MCMC) to the trans-dimensional case. One of the main challenges in MCMC-based inference is that of simulating from high and trans-dimensional target measures. In such cases, MCMC methods may not adequately traverse the support of the target; the simulation results will be unreliable. We develop population methods to deal with such problems, and give a result proving the uniform ergodicity of these population algorithms, under mild assumptions. This result is used to demonstrate the superiority, in terms of convergence rate, of a population transition kernel over a reversible jump sampler for a Bayesian variable selection problem. We also give an example of a population algorithm for a Bayesian multivariate mixture model with an unknown number of components. This is applied to gene expression data of 1000 data points in six dimensions and it is demonstrated that our algorithm out performs some competing Markov chain samplers.