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

• 成果类型: Article
• 署名作者: Eberle, Andreas; Marinelli, Carlo
• 署名单位: University of Bonn; Free University of Bozen-Bolzano
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-012-0410-y
• 发表日期: 2013
• 页码: 665-701
• 关键词: convergence; THEOREM

摘要

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.