Article

Probability Theory and Related Fields

, Volume 155, Issue 3, pp 665-701

First online:

Quantitative approximations of evolving probability measures and sequential Markov chain Monte Carlo methods

  • Andreas EberleAffiliated withInstitut für Angewandte Mathematik, Universität Bonn Email author 
  • , Carlo MarinelliAffiliated withInstitut für Angewandte Mathematik, Universität BonnFacoltà di Economia, Università di Bolzano

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

We study approximations of evolving probability measures by an interacting particle system. The particle system dynamics is a combination of independent Markov chain moves and importance sampling/resampling steps. Under global regularity conditions, we derive non-asymptotic error bounds for the particle system approximation. In a few simple examples, including high dimensional product measures, bounds with explicit constants of feasible size are obtained. Our main motivation are applications to sequential MCMC methods for Monte Carlo integral estimation.

Keywords

Markov chain Monte Carlo Sequential Monte Carlo Importance sampling Spectral gap Dirichlet forms Functional inequalities Feynman–Kac formula

Mathematics Subject Classification (2000)

65C05 60J25 60B10 47H20 47D08