Weight-Preserving Simulated Tempering
Abstract
Simulated tempering is popular method of allowing MCMC algorithms to move between modes of a multimodal target density {\pi}. One problem with simulated tempering for multimodal targets is that the weights of the various modes change for different inverse-temperature values, sometimes dramatically so. In this paper, we provide a fix to overcome this problem, by adjusting the mode weights to be preserved (i.e., constant) over different inverse-temperature settings. We then apply simulated tempering algorithms to multimodal targets using our mode weight correction. We present simulations in which our weight-preserving algorithm mixes between modes much more successfully than traditional tempering algorithms. We also prove a diffusion limit for an version of our algorithm, which shows that under appropriate assumptions, our algorithm mixes in time O(d [log d]^2).
Cite
@article{arxiv.1808.04782,
title = {Weight-Preserving Simulated Tempering},
author = {Nicholas G. Tawn and Gareth O. Roberts and Jeffrey S. Rosenthal},
journal= {arXiv preprint arXiv:1808.04782},
year = {2019}
}