The next meeting of the

National Seminar on Probability and Statistics

will be held on February 14, 2024, at 2:00 p.m. in Room 503 of the Institute of Mathematics and Informatics.

A talk on:

Computable inference for generalised Wright-Fisher processes

will be delivered by

Nathan Judd (University of Warwick, UK).

Abstract.In this talk, we will introduce a class of [0,1]-valued Markov processes with jumps that, as signals in hidden Markov models, admits a computable (exact) filter. By computable filter we mean that each filtering distribution, i.e., the law of the signal at a time t given the data up to time t, is explicitly and exactly available as a finite mixture of Dirichlet distributions. We exploit the tractability of the Wright-Fisher diffusion, in particular, its infinite-sum transition function and its dual process, as a base to construct a generalised version thereof, for which we derive the (exact, predictive and smoothing) filters of the associated hidden Markov model. In addition, we construct an exact sampling scheme to draw samples from the transition functions of this process.