Bernoulli

  • Bernoulli
  • Volume 25, Number 1 (2019), 310-340.

Error bounds for sequential Monte Carlo samplers for multimodal distributions

Daniel Paulin, Ajay Jasra, and Alexandre Thiery

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Abstract

In this paper, we provide bounds on the asymptotic variance for a class of sequential Monte Carlo (SMC) samplers designed for approximating multimodal distributions. Such methods combine standard SMC methods and Markov chain Monte Carlo (MCMC) kernels. Our bounds improve upon previous results, and unlike some earlier work, they also apply in the case when the MCMC kernels can move between the modes. We apply our results to the Potts model from statistical physics. In this case, the problem of sharp peaks is encountered. Earlier methods, such as parallel tempering, are only able to sample from it at an exponential (in an important parameter of the model) cost. We propose a sequence of interpolating distributions called interpolation to independence, and show that the SMC sampler based on it is able to sample from this target distribution at a polynomial cost. We believe that our method is generally applicable to many other distributions as well.

Article information

Source
Bernoulli, Volume 25, Number 1 (2019), 310-340.

Dates
Received: February 2017
Revised: July 2017
First available in Project Euclid: 12 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.bj/1544605248

Digital Object Identifier
doi:10.3150/17-BEJ988

Zentralblatt MATH identifier
07007209

Keywords
asymptotic variance bound central limit theorem metastability Potts model scale invariance sequential Monte Carlo

Citation

Paulin, Daniel; Jasra, Ajay; Thiery, Alexandre. Error bounds for sequential Monte Carlo samplers for multimodal distributions. Bernoulli 25 (2019), no. 1, 310--340. doi:10.3150/17-BEJ988. https://projecteuclid.org/euclid.bj/1544605248


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Supplemental materials

  • Supplement to “Error bounds for sequential Monte Carlo samplers for multimodal distributions”. Some technical proofs from the paper are given here.