In this chalk and talk seminar I will describe a generic scheme for exploiting multiple processors in a single long MCMC simulation. The method is likely to be useful in particular for problems with computationally intensive likelihood evaluations, or likelihood approximation schemes, such as MCMC-ABC. Such problems appear nowadays in the context of finite sites substitution models and models of ancestry requiring branching genelogies (such as host-parasite models, and models of recombination).
I will describe a second scheme for MCMC, in which the user makes no full likelihood evaluations, but nevertheless gets the exact same samples they would have got had they made full likelihood evaluations. The analysis is based on estimating the separation time of coupled Markov chains, one for the approximate MCMC, and one for the exact.
So far these ideas have been implemented in statistical applications in geoscience, but they are quite generic.