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.
We construct zig-zag processes targeting posterior distributions arising in genetics from the Kingman coalescent and two 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 algorithms, and that it is well suited to parallel computation for coalescent models. Our construction is based on embedding discrete variables into a continuous space; a technique previously employed by coalescent Hamiltonian Monte Carlo algorithms which suffer from implementationally and analytically complex boundary crossings. We demonstrate that the continuous-time zig-zag process avoids similar complications.
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