Abstract
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.
Funding Statement
The first author was supported by the National Science Foundation (NSF) grant DMS-1638521 to the Statistical and Applied Mathematical Sciences Institute (SAMSI) and by NSF research traineeship grant DMS-1045153.
The third author was supported by NSF grant DMS-1638521 to SAMSI and by NSF grant DMS-1407622.
Acknowledgments
The authors express their gratitude to the anonymous referees, an Associate Editor, and the Editor for their valuable input, which enhanced the quality of this paper.
Citation
Joe Marion. Joseph Mathews. Scott C. Schmidler. "Finite-sample complexity of sequential Monte Carlo estimators." Ann. Statist. 51 (3) 1357 - 1375, June 2023. https://doi.org/10.1214/23-AOS2295
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