General techniques for perturbed MCMC on complex targets

Develop general-purpose techniques and perturbation bounds for defining and analyzing perturbed Markov chains targeting complex, non-product-form statistical models where straightforward plug-in estimators are unavailable and likelihood evaluation costs may grow superlinearly with data size; in particular, construct methods that yield quantitative bounds on the bias introduced by such perturbations.

Background

The chapter discusses that for complex targets, unlike simple product-form posteriors, there are no straightforward plug-in estimators and computation costs can scale superlinearly, making subsampling both more valuable and harder. Although several case-specific examples exist, the authors highlight the lack of general techniques to systematically design and analyze perturbed chains in this regime.

They explicitly note that establishing such techniques and bounds has been identified as a central open problem in the literature, underscoring both its importance and current lack of resolution.