Weight-preserving simulated tempering

Simulated tempering is a popular method of allowing MCMC algorithms to move between modes of a multimodal target density $$\pi $$ π . 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 $$O(d [\log d]^2)$$ O ( d [ log d ] 2 ) .