The Random Walk Metropolis (RWM) is a simple and enduring Markov chain-based algorithm for approximate simulation from an intractable ‘target’ probability distribution. In this work, we study quantitatively the convergence of this algorithm, providing non-asymptotic estimates on mixing times, with explicit dependence on dimension and other problem parameters. The results hold at a reasonable level of generality, and are often sharp in a suitable sense.

The focus of the talk will be conceptual rather than technical, with an eye towards enabling intuition for i) which high-level aspects of the target distribution influence the convergence behaviour of RWM, and ii) which concrete properties must be verified in order to obtain a rigorous proof. No prior knowledge of the RWM is required from the audience.