Optimal approximating Markov chains for Bayesian inference

Understand

The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis.

• It is common to control computation time by making approximations to the Markov transition kernel.
• Comparatively little attention has been paid to computational optimality in these approximating Markov Chains, or when such approximations are justified relative to obtaining shorter paths from the exact kernel.
• We give simple, sharp bounds for uniform approximations of uniformly mixing Markov chains.