Jump Markov Chains and Rejection-Free Metropolis Algorithms
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We consider versions of the Metropolis algorithm which avoid the inefficiency of rejections. We first illustrate that a natural Uniform Selection Algorithm might not converge to the correct distribution. We then analyse the use of Markov jump chains which avoid successive repetitions of the same state. After exploring the properties of jump chains, we show how they can exploit parallelism in computer hardware to produce more efficient samples. We apply our results to the Metropolis algorithm, to Parallel Tempering, and to a two-dimensional ferromagnetic 4×4 Ising model.
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