Fast Markov Chain Monte Carlo Algorithms via Lie Groups
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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 two new MCMC algorithms. The convergence properties of these new algorithms successively improve on the state of the art. We illustrate the new algorithms with explicit numerical computations, and we empirically demonstrate the improved convergence on a spin glass.
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