Langevin-Type Models II: Self-Targeting Candidates for MCMC Algorithms*
Langevin-Type Models II: Self-Targeting Candidates for MCMC Algorithms*
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Langevin 型模型 II：MCMC 算法的自我定位候选者*
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
R. Tweedie
中科院分区：
文献类型：
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作者：
O. Stramer;R. Tweedie
用于估计分布 π 的 Metropolis-Hastings 算法基于选择候选马尔可夫链，然后接受或拒绝候选者的移动以产生已知以 π 作为不变测度的链。传统方法使用的候选者基本上与 π 无关。我们展示了第一部分（Stramer 和 Tweedie 1999）中开发的候选分布类别，它“自我瞄准”π 的高密度区域，产生的 Metropolis-Hastings 算法的收敛速度似乎比已知的传统候选选择（例如随机游走）的算法要好得多。我们通过指数尾部和多项式尾部的示例以及使用吉布斯采样算法的逻辑回归模型来说明这种行为。详细的结果是在一维中给出的，但我们指出了它们如何成功地扩展到更高的维度。
The Metropolis-Hastings algorithm for estimating a distribution π is based on choosing a candidate Markov chain and then accepting or rejecting moves of the candidate to produce a chain known to have π as the invariant measure. The traditional methods use candidates essentially unconnected to π. We show that the class of candidate distributions, developed in Part I (Stramer and Tweedie 1999), which “self-target” towards the high density areas of π, produce Metropolis-Hastings algorithms with convergence rates that appear to be considerably better than those known for the traditional candidate choices, such as random walk. We illustrate this behavior for examples with exponential and polynomial tails, and for a logistic regression model using a Gibbs sampling algorithm. The detailed results are given in one dimension but we indicate how they may extend successfully to higher dimensions.