Non-reversible guided Metropolis kernel

Pub Date : 2023-04-12 DOI:10.1017/jpr.2022.109
K. Kamatani, Xiaolin Song
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引用次数: 3

Abstract

Abstract We construct a class of non-reversible Metropolis kernels as a multivariate extension of the guided-walk kernel proposed by Gustafson (Statist. Comput. 8, 1998). The main idea of our method is to introduce a projection that maps a state space to a totally ordered group. By using Haar measure, we construct a novel Markov kernel termed the Haar mixture kernel, which is of interest in its own right. This is achieved by inducing a topological structure to the totally ordered group. Our proposed method, the $\Delta$ -guided Metropolis–Haar kernel, is constructed by using the Haar mixture kernel as a proposal kernel. The proposed non-reversible kernel is at least 10 times better than the random-walk Metropolis kernel and Hamiltonian Monte Carlo kernel for the logistic regression and a discretely observed stochastic process in terms of effective sample size per second.
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非可逆引导Metropolis内核
摘要我们构造了一类不可逆的Metropolis核,作为Gustafson(Statist.Comput.81998)提出的引导行走核的多变量扩展。我们方法的主要思想是引入一个投影,将状态空间映射到一个完全有序的群。利用Haar测度,我们构造了一个新的马尔可夫核,称为Haar混合核,它本身就很有意义。这是通过将拓扑结构引入全序群来实现的。我们提出的方法,$\Delta$引导的Metropolis–Haar内核,是通过使用Haar混合内核作为建议内核来构建的。就每秒有效样本量而言,对于逻辑回归和离散观测随机过程,所提出的不可逆核至少是随机行走Metropolis核和Hamiltonian蒙特卡罗核的10倍。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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