  Simulated Tempering (ST) is an MCMC algorithm for complex target
distributions that operates on a path between the target and a more amenable
reference distribution. Crucially, if the reference enables i.i.d. sampling, ST
is regenerative and can be parallelized across independent tours. However, the
difficulty of tuning ST has hindered its widespread adoption. In this work, we
develop a simple nonreversible ST (NRST) algorithm, a general theoretical
analysis of ST, and an automated tuning procedure for ST. A core contribution
that arises from the analysis is a novel performance metric -- Tour
Effectiveness (TE) -- that controls the asymptotic variance of estimates from
ST for bounded test functions. We use the TE to show that NRST dominates its
reversible counterpart. We then develop an automated tuning procedure for NRST
algorithms that targets the TE while minimizing computational cost. This
procedure enables straightforward integration of NRST into existing
probabilistic programming languages. We provide extensive experimental evidence
that our tuning scheme improves the performance and robustness of NRST
algorithms on a diverse set of probabilistic models.
