Open Access
February 2019 Error bounds for sequential Monte Carlo samplers for multimodal distributions
Daniel Paulin, Ajay Jasra, Alexandre Thiery
Bernoulli 25(1): 310-340 (February 2019). DOI: 10.3150/17-BEJ988


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.


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Daniel Paulin. Ajay Jasra. Alexandre Thiery. "Error bounds for sequential Monte Carlo samplers for multimodal distributions." Bernoulli 25 (1) 310 - 340, February 2019.


Received: 1 February 2017; Revised: 1 July 2017; Published: February 2019
First available in Project Euclid: 12 December 2018

zbMATH: 07007209
MathSciNet: MR3892321
Digital Object Identifier: 10.3150/17-BEJ988

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

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

Vol.25 • No. 1 • February 2019
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