We present a general framework for accelerating a large class of widely used
Markov chain Monte Carlo (MCMC) algorithms. Our approach exploits fast,
iterative approximations to the target density to speculatively evaluate many
potential future steps of the chain in parallel. The approach can accelerate
computation of the target distribution of a Bayesian inference problem, without
compromising exactness, by exploiting subsets of data. It takes advantage of
whatever parallel resources are available, but produces results exactly
equivalent to standard serial execution. In the initial burn-in phase of chain
evaluation, it achieves speedup over serial evaluation that is close to linear
in the number of available cores