On swapping and simulated tempering algorithms

Zheng, Zhongrong

doi:10.1016/s0304-4149(02)00232-6

Cited by 15 publications

(10 citation statements)

References 18 publications

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“…However, they do capture some important qualitative features of more complex and more realistic models, and for this reason increase our optimism that the swapping method is efficient for wider classes of problems. Our intuition is also supported by Zheng [29,30], who proves that in fairly general situations the spectral gap of the simulated tempering chain is bounded below by a multiple of the gap of the associated swapping chain.…”

Section: J͒ Where Z Is the Normalizing Constant Observe That Assupporting

confidence: 67%

On the swapping algorithm

Madras

Zheng

2002

Random Struct Algorithms

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Section: J͒ Where Z Is the Normalizing Constant Observe That Assupporting

confidence: 67%

On the swapping algorithm

Madras

Zheng

2002

Random Struct Algorithms

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“…We will show that our overlap quantity δ(A) is bounded below by the overlap used in Madras and Randall [14] and Zheng [29], and that our definition is equal to theirs in the case of π symmetric (as defined in Section 4.1).…”

Section: 2mentioning

confidence: 93%

Conditions for rapid mixing of parallel and simulated tempering on multimodal distributions

Woodard¹,

Schmidler²,

Huber³

2009

Ann. Appl. Probab.

111

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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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“…Due to our experience with more advanced single chain MCMC methods (such as tempered transitions (Neal 1996) and delayed rejection (Green and Mira 2001); see Jasra et al 2005a for examples), it seems clear that alternative methods are needed. Note that one single chain method, simulated tempering (Marinari and Parisi 1992;Geyer and Thompson 1995), can perform better than some population MCMC schemes discussed below (see Zheng 2003), if the pseudo prior can be estimated accurately (this is typically a high dimensional integral which can be estimated on the fly using stochastic approximation; see Atchadé and Liu 2004). However, in some of the applications for which population methods are required (e.g.…”

Section: Example: Mixture Modellingmentioning

confidence: 99%

On population-based simulation for static inference

2007

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In this paper we present a review of populationbased simulation for static inference problems. Such methods can be described as generating a collection of random variables {X n } n=1,...,N in parallel in order to simulate from some target density π (or potentially sequence of target densities). Population-based simulation is important as many challenging sampling problems in applied statistics cannot be dealt with successfully by conventional Markov chain Monte Carlo (MCMC) methods. We summarize population-based MCMC (Geyer, Computing Science and Statistics: The 23rd Symposium on the Interface, pp. 156-163, 1991; Liang and Wong, J. Am. Stat. Assoc. 96, 653-666, 2001) and sequential Monte Carlo samplers (SMC) (Del Moral, Doucet and Jasra, J. Roy. Stat. Soc. Ser. B 68, 411-436, 2006a), providing a comparison of the approaches. We give numerical examples from Bayesian mixture modelling (Richardson and Green, J. Roy. Stat. Soc. Ser. B 59, 731-792, 1997).

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On swapping and simulated tempering algorithms

Cited by 15 publications

References 18 publications

On the swapping algorithm

On the swapping algorithm

Conditions for rapid mixing of parallel and simulated tempering on multimodal distributions

On population-based simulation for static inference

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