FINITE-SAMPLE COMPLEXITY OF SEQUENTIAL MONTE CARLO ESTIMATORS

• 成果类型: Article
• 署名作者: Marion, Joe; Mathews, Joseph; Schmidler, Scott C.
• 署名单位: Duke University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/23-AOS2295
• 发表日期: 2023
• 页码: 1357-1375
• 关键词: CENTRAL-LIMIT-THEOREM; logconcave functions; error-bounds; parallel; filters; approximations; algorithms; STABILITY

摘要

We present bounds for the finite-sample error of sequential Monte Carlo samplers on static spaces. Our approach explicitly relates the performance of the algorithm to properties of the chosen sequence of distributions and mixing properties of the associated Markov kernels. This allows us to give the first finite-sample comparison to other Monte Carlo schemes. We obtain bounds for the complexity of sequential Monte Carlo approximations for a variety of target distributions such as finite spaces, product measures and log-concave distributions including Bayesian logistic regression. The bounds obtained are within a logarithmic factor of similar bounds obtainable for Markov chain Monte Carlo.