A tutorial on adaptive MCMC
A tutorial on adaptive MCMC
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DOI：
10.1007/s11222-008-9110-y
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发表时间：
2008-12-01
影响因子：
2.2
通讯作者：
Thoms, Johannes
中科院分区：
文献类型：
--
作者：
Andrieu, Christophe;Thoms, Johannes
我们审查自适应马尔可夫链蒙特卡罗算法（MCMC）作为一种手段，以优化其性能。使用简单的玩具的例子，我们回顾他们的理论基础，特别是显示为什么自适应MCMC算法可能会失败时，一些基本属性不满足。这导致了关于正确算法设计的指导方针。然后，我们审查标准和有用的框架随机逼近，它允许一个系统地优化一般使用的标准，但也分析自适应MCMC算法的属性。然后，我们提出了一系列新的自适应算法，在实践中证明是强大的和可靠的。这些算法适用于人工和高维场景，也适用于经典的矿难数据集推理问题。
We review adaptive Markov chain Monte Carlo algorithms (MCMC) as a mean to optimise their performance. Using simple toy examples we review their theoretical underpinnings, and in particular show why adaptive MCMC algorithms might fail when some fundamental properties are not satisfied. This leads to guidelines concerning the design of correct algorithms. We then review criteria and the useful framework of stochastic approximation, which allows one to systematically optimise generally used criteria, but also analyse the properties of adaptive MCMC algorithms. We then propose a series of novel adaptive algorithms which prove to be robust and reliable in practice. These algorithms are applied to artificial and high dimensional scenarios, but also to the classic mine disaster dataset inference problem.