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Fast Markov Chain Monte Carlo Algorithms via Lie Groups

Published 24 Jan 2019 in math.ST, math.GR, math.RA, stat.CO, and stat.TH | (1901.08606v2)

Abstract: From basic considerations of the Lie group that preserves a target probability measure, we derive the Barker, Metropolis, and ensemble Markov chain Monte Carlo (MCMC) algorithms, as well as variants of waste-recycling Metropolis-Hastings and an altogether new MCMC algorithm. We illustrate these constructions with explicit numerical computations, and we empirically demonstrate on a spin glass that the new algorithm converges more quickly than its siblings.

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