Bernoulli factories and duality for general Wright-Fisher and coalescent processes

Koskela Jere, Newcastle University
Łatuszyński Krzysztof, University of Warwick
Spanò Dario, University of Warwick

Wright-Fisher diffusions and branching-coalescing particle systems are central models in time-evolving Bayesian inference and mathematical population genetics. Prominent examples include the Kingman coalescent and the Wright-Fisher diffusion with linear drift, as well as the ancestral selection graph and the diffusion with quadratic drift. Both of these pairs satisfying a duality relation which yields equations for expectations of functionals. I will show how branching-coalescing duals can be constructed for Wright-Fisher diffusions with a very broad class of drift functions. The key tool is the Bernoulli factory, which is a family of computational methods for simulating events with intractable probabilities.

Area: CS59 - Dependent random measures: evolution and inference (Dario Spanò)

Keywords: Bernoulli factory, duality, genealogical process, Wright-Fisher diffusion

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