On connections between sequential Bayesian inference and evolutionary dynamics

Abstract

It has long been posited that there is a connection between the dynamical equations describing evolutionary processes in biology and sequential Bayesian learning methods. This talk describes new research in which this precise connection is rigorously established in the continuous time setting.  Here we focus on a class of interacting particle methods for solving the sequential Bayesian inference problem which are characterised by a McKean-Vlasov SDE. Of particular importance is a piecewise smooth approximation of the observation path from which the discrete time filtering equations are shown to converge to a Stratonovich interpretation of the Kushner equation. This smooth formulation will then be used to draw precise connections between nonlinear filtering and replicator-mutator dynamics.  Additionally, gradient flow formulations will be investigated as well as a form of replicator-mutator dynamics which is shown to be beneficial for the misspecified filtering problem.  It is hoped this work will spur further research into exchanges between sequential learning and evolutionary biology and to inspire new algorithms in filtering and sampling.