Explicit convergence bounds for Metropolis Markov chains
I will present recent work with C. Andrieu, A. Lee and A. Wang giving explicit bounds for L2-mixing times and the first explicit bounds for the spectral gap for Metropolis Markov chains on R^d. In particular, we study the Random Walk Metropolis (RWM) Markov chain with arbitrary proposal variances and in any dimension. We obtain the correct scaling with dimension for sufficiently regular target distributions. Our positive results are quite generally applicable. We also study the preconditioned Crank--Nicolson Markov chain, obtaining dimension-independent bounds under suitable assumptions.
Preprint available at https://arxiv.org/abs/2211.08959.