UBC - University of British Columbia (Vancouver Campus, , 2329 West Mall, Vancouver, BC, V6T 1Z4 /
Okanagan Campus, 3333 University Way, Kelowna, BC, V1V 1V7 - Canada)
UBC - University of British Columbia (Vancouver Campus, , 2329 West Mall, Vancouver, BC, V6T 1Z4 /
Okanagan Campus, 3333 University Way, Kelowna, BC, V1V 1V7 - Canada)
Abstract : We present a new interacting Markov chain Monte Carlo methodology for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast to traditional Markov chains, their time evolution may depend on the occupation measure of the past values. This general methodology allows us to provide a natural way to sample from a sequence of target probability measures of increasing complexity. We develop an original theoretical analysis to analyze the behaviour of these algorithms as the time parameter tends to infinity. This analysis relies on measure-valued processes and semigroup techniques. We present a variety of convergence results including exponential estimates and a uniform convergence theorem with respect to the number of target distributions, yielding what seems to be the first results of this kind for this class of self-interacting models. We also illustrate these models in the context of Feynman-Kac distribution flows.
https://hal.inria.fr/inria-00227508 Contributor : Pierre Del MoralConnect in order to contact the contributor Submitted on : Tuesday, February 5, 2008 - 11:24:54 AM Last modification on : Friday, February 4, 2022 - 3:23:51 AM Long-term archiving on: : Friday, November 25, 2016 - 8:48:29 PM
Pierre del Moral, Arnaud Doucet. Interacting Markov Chain Monte Carlo Methods For Solving Nonlinear Measure-Valued Equations. Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2010, 20 (2), pp.593-639. ⟨inria-00227508v4⟩