Rate-optimal refinement strategies for local approximation MCMC

Many Bayesian inference problems involve target distributions whose density functions are computationally expensive to evaluate. Replacing the with a local approximation based on small number of carefully chosen evaluations can significantly reduce computational expense Markov chain Monte Carlo (MCMC) sampling. Moreover, continual refinement guarantee asymptotically exact We devise new strategy for balancing decay rate bias due that MCMC variance. prove error resulting (LA-MCMC) algorithm decays at roughly expected $$1/\sqrt{T}$$ rate, and we demonstrate this numerically. also introduce an algorithmic parameter guarantees convergence given very weak tail bounds, strengthening previous results. Finally, apply LA-MCMC intensive inverse problem arising in groundwater hydrology.