Error bounds for sequential Monte Carlo samplers for multimodal distributions

Daniel Paulin, Ajay Jasra, Alexandre Thiery

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)310-340
Number of pages31
JournalBernoulli - Journal of the Bernoulli Society (Bernoulli)
Issue number1
Publication statusPublished - 1 Feb 2019
Externally publishedYes


Dive into the research topics of 'Error bounds for sequential Monte Carlo samplers for multimodal distributions'. Together they form a unique fingerprint.

Cite this