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Zig-zag sampling for discrete structures and non-reversible phylogenetic MCMC

By Jere Koskela


We construct a zig-zag process targeting posterior distributions arising in genetics from the Kingman coalescent and several popular models of mutation. We show that the zig-zag process can lead to efficiency gains of up to several orders of magnitude over classical Metropolis-Hastings, and argue that it is also well suited to parallel computation for coalescent models. Our construction is based on embedding discrete variables into continuous space; a technique previously exploited in the construction of Hamiltonian Monte Carlo algorithms, where it can lead to implementationally and analytically complex boundary crossings. We demonstrate that the continuous-time zig-zag process can largely avoid these complications.Comment: 20 pages, 6 figure

Topics: Statistics - Computation, Mathematics - Statistics Theory, Quantitative Biology - Populations and Evolution, Statistics - Methodology, 62M05 (Primary) 60J25, 92D15 (Secondary)
Year: 2020
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