Comparison of Markov chains via weak Poincaré inequalities with application to pseudo-marginal MCMC
通过弱庞加莱不等式比较马尔可夫链及其伪边际 MCMC 应用
We investigate the use of a certain class of functional inequalities known as weak Poincaré 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…