Finite-sample complexity of sequential Monte Carlo estimators
Joe Marion, Joseph Mathews, Scott C. Schmidler
The Annals of Statistics · 2023 · Volume 51 · Issue 3
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.
Keywords
60J22, 65C60, 65C60, Bayesian computation, computational complexity, sequential Monte Carlo
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