Nested Sequential Monte Carlo Methods

Christian A. Naesseth; Fredrik Lindsten; Thomas B. Schön

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arXiv · 1502.02536

Nested Sequential Monte Carlo Methods

Christian A. Naesseth·Fredrik Lindsten·Thomas B. Schön

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Abstract

We propose nested sequential Monte Carlo (NSMC), a methodology to sample from sequences of probability distributions, even where the random variables are high-dimensional. NSMC generalises the SMC framework by requiring only approximate, properly weighted, samples from the SMC proposal distribution, while still resulting in a correct SMC algorithm. Furthermore, NSMC can in itself be used to produce such properly weighted samples. Consequently, one NSMC sampler can be used to construct an efficient high-dimensional proposal distribution for another NSMC sampler, and this nesting of the algorithm can be done to an arbitrary degree. This allows us to consider complex and high-dimensional models using SMC. We show results that motivate the efficacy of our approach on several filtering problems with dimensions in the order of 100 to 1 000.

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BibTeX RIS

Christian A. Naesseth, Fredrik Lindsten, Thomas B. Schön. 2015-09-11. Nested Sequential Monte Carlo Methods. https://arxiv.org/abs/1502.02536

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