Upper and lower bounds on the subgeometric convergence of adaptive Markov chain Monte Carlo (opens in new tab)

We investigate lower bounds on the subgeometric convergence of adaptive Markov chain Monte Carlo under any adaptation strategy. In particular, we prove general lower bounds in total variation and on the weak convergence rate under general adaptation plans. If the adaptation diminishes sufficiently fast, we also develop comparable convergence rate upper bounds that are capable of approximately matching the convergence rate in the subgeometric...