Title: Fast Markov Chain Monte Carlo Algorithms via Lie Groups,
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 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.