Comparison of Markov chains via weak Poincar\'e inequalities with application to pseudo-marginal MCMC. (arXiv:2112.05605v2 [stat.CO] UPDATED)

We investigate the use of a certain class of functional inequalities known as
weak Poincar\'e inequalities to bound convergence of Markov chains to
equilibrium. We show that this enables the straightforward and transparent
derivation of subgeometric convergence bounds for methods such as the
Independent Metropolis--Hastings sampler and pseudo-marginal methods for
intractable likelihoods, the latter being subgeometric in many practical
settings. These results rely on novel quantitative comparison theorems between
Markov chains. Associated proofs are simpler than those relying on
drift/minorization …

application arxiv comparison markov mcmc