# Error Bounds for Sequential Monte Carlo Samplers for Multimodal Distributions

arXiv: https://arxiv.org/abs/1509.08775 · HTML: https://mlsanity.com/paper/1509.08775/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Sep 2015.

## Built on by (most cited first, 4 of 4)

- [Provable Convergence and Limitations of Geometric Tempering for Langevin Dynamics](https://mlsanity.com/paper/2410.09697/) (2024)
- [Goal-Oriented Bayesian Optimal Experimental Design for Nonlinear Models using Markov Chain Monte Carlo](https://mlsanity.com/paper/2403.18072/) (2024)
- [Convergence Bounds for Sequential Monte Carlo on Multimodal Distributions using Soft Decomposition](https://mlsanity.com/paper/2405.19553/) (2024)
- [Finite Sample Complexity of Sequential Monte Carlo Estimators on Multimodal Target Distributions](https://mlsanity.com/paper/2208.06672/) (2022)

## Abstract (arXiv)

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.