Abstract
Developing efficient MCMC algorithms is indispensable in Bayesian inference. In parallel tempering, multiple interacting MCMC chains run to more efficiently explore the state space and improve performance. The multiple chains advance independently through local moves, and the performance enhancement steps are exchange moves, where the chains pause to exchange their current sample amongst each other. To accelerate the independent local moves, they may be performed simultaneously on multiple processors. Another problem is then encountered: depending on the MCMC implementation and inference problem, local moves can take a varying and random amount of time to complete. There may also be infrastructure-induced variations, such as competing jobs on the same processors, which arises in cloud computing. Before exchanges can occur, all chains must complete the local moves they are engaged in to avoid introducing a potentially substantial bias (Proposition 1). To solve this issue of randomly varying local move completion times in multi-processor parallel tempering, we adopt the Anytime Monte Carlo framework of (Murray, L. M., Singh, S., Jacob, P. E., and Lee, A.: Anytime Monte Carlo. arXiv preprintarXiv:1612.03319, (2016): we impose real-time deadlines on the parallel local moves and perform exchanges at these deadlines without any processor idling. We show our methodology for exchanges at real-time deadlines does not introduce a bias and leads to significant performance enhancements over the naïve approach of idling until every processor’s local moves complete. The methodology is then applied in an ABC setting, where an Anytime ABC parallel tempering algorithm is derived for the difficult task of estimating the parameters of a Lotka–Volterra predator-prey model, and similar efficiency enhancements are observed.
Highlights
Consider a set of m observations y = {y1, . . . , ym} ∈ Y following a probability model with underlying parameters θ ∈ and associated likelihood f (y1, . . . , ym | θ ) which we abbreviate to f (y | θ )
We show that we can improve the performance of the 1-hit Markov chain Monte Carlo (MCMC) kernel by introducing tempering and exchange moves, and embed the resulting parallel tempering algorithm within the Anytime framework to mitigate processor idling due to random local move completion times
In an effort to increase the efficiency of MCMC algorithms, in particular for use on multiple processors, and for situations in which compute times of the algorithms depend on their
Summary
Ym} ∈ Y following a probability model with underlying parameters θ ∈ and associated likelihood f B Alix Marie d’Avigneau random walk proposals, for example. As models become more complex, the exploration of the posterior using such basic methods quickly becomes inefficient (Beskos et al (2009)). Initially proposed by Swendsen and Wang (1986) and further developed under the name Metropolis-coupled Markov chain Monte Carlo (MC) by Geyer (1991), is a generic method for improving the efficiency of MCMC that can be very effective without significantly altering the original MCMC algorithm, beyond perhaps tuning its local proposals for each temperature. The parallel tempering algorithm runs multiple interacting MCMC chains to more efficiently explore the state space. The multiple MCMC chains are advanced independently, in what is known as the
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