A0811
Title: Filtering Wright-Fisher diffusions via discrete dual processes
Authors: Paul Jenkins - University of Warwick (United Kingdom)
Matteo Ruggiero - University of Torino (Italy)
Guillaume Kon Kam King - Université Paris-Saclay, INRAE (France) [presenting]
Abstract: Exact inference for hidden Markov models requires the evaluation of all distributions of interest, filtering, prediction, smoothing, and likelihood with a finite computational effort. We provide sufficient conditions for exact inference for a class of hidden Markov models on general state spaces, given a set of discretely collected indirect observations nonlinearly linked to the signal, and a set of practical inference algorithms. The conditions we obtain are concerned with the existence of a certain type of dual process, which is an auxiliary process embedded in the time reversal of the signal, that in turn allows us to represent the distributions and functions of interest as countable mixtures of elementary densities or products thereof. We explore the applicability of this strategy for exact inference on Wright-Fisher diffusions, with or without selection.
