Conditions for Rapid Mixing of Parallel and Simulated Tempering on Multimodal Distributions
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2009
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Abstract
We give conditions under which a Markov chain constructed via parallel or simulated tempering is guaranteed to be rapidly mixing, which are applicable to a wide range of multimodal distributions arising in Bayesian statistical inference and statistical mechanics. We provide lower bounds on the spectral gaps of parallel and simulated tempering. These bounds imply a single set of sufficient conditions for rapid mixing of both techniques. A direct consequence of our results is rapid mixing of parallel and simulated tempering for several normal mixture models, and for the mean-field Ising model.
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Scholars@Duke
![Schmidler](https://scholars.duke.edu/profile-images/thumbnail200/0271040.jpg)
Scott C. Schmidler
Research Interests:
- Monte Carlo methods; high-dimensional sampling algorithms; Mixing times of Markov chains; MCMC; Sequential Monte Carlo; probabilistic graphical models; Bayesian computation; Computational complexity of statistical inference.
- Computational biology; Protein structure and folding; computational immunology; computational biophysics; statistical physics; computational statistical mechanics; molecular evolution.
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