One of the simplest and most powerful practical uses of the ergodic theory of Markov chains is in Markov chain Monte Carlo (MCMC). Suppose we wish to simulate from a probability density π (which will be called the target density) but that direct simulation is either impossible or practically infeasible (possibly due to the high dimensionality of π). This generic problem occurs in diverse scient...

Markov chain Monte Carlo (MCMC) algorithms are generally regarded as the gold standard technique for Bayesian inference. They theoretically well-understood and conceptually simple to apply in practice. The drawback of MCMC is that performing exact inference requires all data be processed at each iteration algorithm. For large datasets, computational cost can prohibitive, which has led recent de...