Weight-preserving simulated tempering

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Abstract

Simulated tempering is a popular method of allowing MCMC algorithms to move between modes of a multimodal target density 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).

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Tawn, N. G., Roberts, G. O., & Rosenthal, J. S. (2020). Weight-preserving simulated tempering. Statistics and Computing, 30(1), 27–41. https://doi.org/10.1007/s11222-019-09863-3

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