Probability Theory and Related Fields

, Volume 155, Issue 3, pp 665–701

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

Authors

    • Institut für Angewandte MathematikUniversität Bonn
  • Carlo Marinelli
    • Institut für Angewandte MathematikUniversität Bonn
    • Facoltà di EconomiaUniversità di Bolzano
Article

DOI: 10.1007/s00440-012-0410-y

Cite this article as:
Eberle, A. & Marinelli, C. Probab. Theory Relat. Fields (2013) 155: 665. doi:10.1007/s00440-012-0410-y

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 CarloSequential Monte CarloImportance samplingSpectral gapDirichlet formsFunctional inequalitiesFeynman–Kac formula

Mathematics Subject Classification (2000)

65C0560J2560B1047H2047D08

Copyright information

© Springer-Verlag 2012