On a Class of Genealogical and Interacting Metropolis Models
A genealogical tree based particle model for drawing approximate samples from the conditional path-distributions of a Markov chain with respect to its terminal values is presented. This path-particle evolution model can be interpreted as the historical process associated to a sequence of interacting Metropolis Markov chains. This novel class of interacting models can also be used to obtain approximate samples from a given target distribution which is only known up to a normalizing constant. We design an original Feynman–Kac modeling technique for studying the asymptotic analysis of these path-particle and Metropolis type simulation models. We provide precise convergence results as the time or the size of the systems tends to infinity. In contrast to the traditional Metropolis model we show that the decays to equilibrium do not depend on the nature of the desired limiting distribution.