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Adaptive Incremental Mixture Markov chain Monte Carlo
Journal of Computational and Graphical Statistics ( IF 2.4 ) Pub Date : 2019-06-07 , DOI: 10.1080/10618600.2019.1598872
Florian Maire 1 , Nial Friel 2, 3 , Antonietta Mira 4, 5 , Adrian E Raftery 6
Affiliation  

Abstract We propose adaptive incremental mixture Markov chain Monte Carlo (AIMM), a novel approach to sample from challenging probability distributions defined on a general state-space. While adaptive MCMC methods usually update a parametric proposal kernel with a global rule, AIMM locally adapts a semiparametric kernel. AIMM is based on an independent Metropolis–Hastings proposal distribution which takes the form of a finite mixture of Gaussian distributions. Central to this approach is the idea that the proposal distribution adapts to the target by locally adding a mixture component when the discrepancy between the proposal mixture and the target is deemed to be too large. As a result, the number of components in the mixture proposal is not fixed in advance. Theoretically, we prove that there exists a stochastic process that can be made arbitrarily close to AIMM and that converges to the correct target distribution. We also illustrate that it performs well in practice in a variety of challenging situations, including high-dimensional and multimodal target distributions. Finally, the methodology is successfully applied to two real data examples, including the Bayesian inference of a semiparametric regression model for the Boston Housing dataset. Supplementary materials for this article are available online.

中文翻译:

自适应增量混合马尔可夫链蒙特卡罗

摘要 我们提出了自适应增量混合马尔可夫链蒙特卡洛 (AIMM),这是一种从定义在一般状态空间上的具有挑战性的概率分布进行采样的新方法。自适应 MCMC 方法通常使用全局规则更新参数提议内核,而 AIMM 局部调整半参数内核。AIMM 基于独立的 Metropolis-Hastings 提议分布,该分布采用高斯分布的有限混合形式。这种方法的核心思想是,当提议混合与目标之间的差异被认为太大时,提议分布通过局部添加混合组件来适应目标。因此,混合提议中的组件数量不是预先固定的。理论上,我们证明存在一个可以任意接近 AIMM 并且收敛到正确目标分布的随机过程。我们还说明它在各种具有挑战性的情况下在实践中表现良好,包括高维和多模态目标分布。最后,该方法成功地应用于两个真实数据示例,包括波士顿住房数据集的半参数回归模型的贝叶斯推理。本文的补充材料可在线获取。包括波士顿住房数据集的半参数回归模型的贝叶斯推理。本文的补充材料可在线获取。包括波士顿住房数据集的半参数回归模型的贝叶斯推理。本文的补充材料可在线获取。
更新日期:2019-06-07
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