Woodard, DBSchmidler, SCHuber, M2011-06-212011-06-212009Woodard,Dawn B.;Schmidler,Scott C.;Huber,Mark. 2009. Conditions for Rapid Mixing of Parallel and Simulated Tempering on Multimodal Distributions. Annals of Applied Probability 19(2): 617-640.1050-5164https://hdl.handle.net/10161/4407We 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.en-USmarkov chain monte carlotemperingrapidly mixing markov chainsspectral gapmetropolis algorithmmarkov-chainsmonte-carloconvergencestatistics & probability