## Conditional distribution of Wright-Fisher diffusions given genealogy-type data

We consider a statistical model where Wright-Fisher diffusions are interpreted as random parameters drawn from the prior on their path space, and data are given by the genealogy associated to a random sample from the underlying population. We characterize conditional Wright-Fisher diffusions given these type of data and show they are inhomogeneous Wright-Fisher diffusions with drift given by piecewise constant functions which depend on the data. We thus establish conjugacy for this Bayesian categorical model on the path space, which marginally in time reduces to the well-known conjugacy of the Dirichlet-categorical model.

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

Keywords: Bayesian inference; time-dependent analysis; population genetics

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