Anytime parallel tempering

Developing efficient MCMC algorithms is indispensable in Bayesian inference. In parallel tempering, multiple interacting chains run to more efficiently explore the state space and improve performance. The advance independently through local moves, performance enhancement steps are exchange where pause their current sample amongst each other. To accelerate independent they may be performed simultaneously on processors. Another problem then encountered: depending implementation inference problem, moves can take a varying random amount of time complete. There also infrastructure-induced variations, such as competing jobs same processors, which arises cloud computing. Before exchanges occur, all must complete engaged avoid introducing potentially substantial bias (Proposition 2.1). solve this issue randomly move completion times multi-processor we adopt Anytime Monte Carlo framework Murray et al. (2016): impose real-time deadlines perform at these without any processor idling. We show our methodology for does not introduce leads significant enhancements over na\"ive approach idling until every processor's applied an ABC setting, tempering algorithm derived difficult task estimating parameters Lotka-Volterra predator-prey model, similar efficiency observed.