Non-reversible guided Metropolis kernel
Non-reversible guided Metropolis kernel
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不可逆引导 Metropolis 内核
DOI：
10.1017/jpr.2022.109
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发表时间：
2023
影响因子：
1
通讯作者：
Song Xiaolin
中科院分区：
文献类型：
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作者：
Kamatani Kengo;Song Xiaolin
我们构造了一类不可逆的大都会核作为Gustafson（Statistist. Comput. 8，1998）。我们的方法的主要思想是引入一个投影，将一个状态空间映射到一个全序群。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，这是在其本身的权利感兴趣。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，引导大都市哈尔内核，构造使用哈尔混合内核作为建议内核。对于Logistic回归和离散观测的随机过程，所提出的不可逆核比随机行走大都会核和Hamiltonian Monte Carlo核的每秒有效样本量至少好10倍.
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 -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.