Non-reversible guided Metropolis kernel

IF 0.7 4区 数学 Q3 STATISTICS & PROBABILITY
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.
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。
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来源期刊
Journal of Applied Probability
Journal of Applied Probability 数学-统计学与概率论
CiteScore
1.50
自引率
10.00%
发文量
92
审稿时长
6-12 weeks
期刊介绍: Journal of Applied Probability is the oldest journal devoted to the publication of research in the field of applied probability. It is an international journal published by the Applied Probability Trust, and it serves as a companion publication to the Advances in Applied Probability. Its wide audience includes leading researchers across the entire spectrum of applied probability, including biosciences applications, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used. A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.
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