摘要翻译:
本文给出了基于群体的马尔可夫链蒙特卡罗(MCMC)在跨维情形下的推广。基于MCMC的推理面临的主要挑战之一是从高维和跨维的目标测度进行模拟。在这种情况下,MCMC方法可能无法充分遍历目标的支持;模拟结果将是不可靠的。我们发展了种群方法来处理这类问题,并在温和的假设下给出了证明这些种群算法一致遍历性的结果。这一结果被用来证明总体转移核在收敛速度方面优于可逆跳变采样器求解贝叶斯变量选择问题。我们还给出了一个具有未知分量数的贝叶斯多元混合模型的种群算法的例子。将该算法应用于六个维度的1000个数据点的基因表达数据,结果表明,该算法能有效地执行一些竞争马尔可夫链采样器。
---
英文标题:
《Population-Based Reversible Jump Markov Chain Monte Carlo》
---
作者:
Ajay Jasra, David A. Stephens and Chris C. Holmes
---
最新提交年份:
2007
---
分类信息:
一级分类:Statistics 统计学
二级分类:Computation 计算
分类描述:Algorithms, Simulation, Visualization
算法、模拟、可视化
--
---
英文摘要:
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.
---
PDF链接:
https://arxiv.org/pdf/711.0186