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Abstract

Many common Markov chain Monte Carlo (MCMC) kernels can be formulated using a deterministic involutive proposal with a step size parameter. Selecting an appropriate step size is often a challenging task in practice; and for complex multiscale targets, there may not be one choice of step size that works well globally. In this work, we address this problem with a novel class of involutive MCMC methods---AutoStep MCMC---that selects an appropriate step size at each iteration adapted to the local geometry of the target distribution. We prove that under mild conditions AutoStep MCMC is π-invariant, irreducible, and aperiodic, and obtain bounds on expected energy jump distance and cost per iteration. Empirical results examine the robustness and e cacy of our proposed step size selection procedure, and show that AutoStep MCMC is competitive with state-of-the-art methods in terms of effective sample size per unit cost on a range of challenging target distributions.