Haar-Weave-Metropolis kernel
Kengo Kamatani, Xiaolin Song

TL;DR
This paper introduces the Haar-Weave-Metropolis kernel, a novel Markov chain Monte Carlo method combining deterministic transforms with Haar measure to improve robustness and convergence, especially for heavy-tailed distributions.
Contribution
It proposes a new Markov kernel that integrates deterministic transforms preserving structure with Haar measure, enhancing global and local information utilization.
Findings
Outperforms existing methods in effective sample size
Achieves higher mean square jump distance per second
Demonstrates robustness for heavy-tailed target distributions
Abstract
Recently, many Markov chain Monte Carlo methods have been developed with deterministic reversible transform proposals inspired by the Hamiltonian Monte Carlo method. The deterministic transform is relatively easy to reconcile with the local information (gradient etc.) of the target distribution. However, as the ergodic theory suggests, these deterministic proposal methods seem to be incompatible with robustness and lead to poor convergence, especially in the case of target distributions with heavy tails. On the other hand, the Markov kernel using the Haar measure is relatively robust since it learns global information about the target distribution introducing global parameters. However, it requires a density preserving condition, and many deterministic proposals break this condition. In this paper, we carefully select deterministic transforms that preserve the structure and create a…
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Taxonomy
TopicsMarkov Chains and Monte Carlo Methods · Gaussian Processes and Bayesian Inference · Bayesian Methods and Mixture Models
