Accelerating parallel tempering: Quantile tempering algorithm (QuanTA). (September 2019)

• Record Type: Journal Article
• Authors: Tawn, Nicholas G.; Roberts, Gareth O.
• Is Part Of: Advances in applied probability. Volume 51:Number 3(2019)
• Page Start: 802
• Page End: 834
• Publication Date: 2019-09
• Subjects: Parallel tempering, -- Metropolis-coupled MCMC, -- accelerated MCMC, -- Markov chain Monte Carlo, -- multimodal, -- population MCMC; Primary 60J22, -- Secondary 65C05, -- 65C60; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2019.35
• Languages: English
• ISSNs: 0001-8678

Abstract

Abstract: It is well known that traditional Markov chain Monte Carlo (MCMC) methods can fail to effectively explore the state space for multimodal problems. Parallel tempering is a well-established population approach for such target distributions involving a collection of particles indexed by temperature. However, this method can suffer dramatically from the curse of dimensionality. In this paper we introduce an improvement on parallel tempering called QuanTA. A comprehensive theoretical analysis quantifying the improved efficiency and scalability of the approach is given. Under weak regularity conditions, QuanTA gives accelerated mixing through the temperature space. Empirical evidence of the effectiveness of this new algorithm is illustrated on canonical examples.