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Parallel tempering (PT) is a class of Markov chain Monte Carlo algorithms that constructs a path of distributions annealing between a tractable reference and an intractable target, and then interchanges states along the path to improve mixing in the target. The performance of PT depends on how quickly a sample from the reference distribution makes its way to the target, which in turn depends on the particular path of annealing distributions. However, past work on PT has used only simple paths constructed from convex combinations of the reference and target log-densities. This paper begins by demonstrating that this path performs poorly in the setting where the reference and target are nearly mutually singular. To address this issue, we expand the framework of PT to general families of paths, formulate the choice of path as an optimization problem that admits tractable gradient estimates, and propose a flexible new family of spline interpolation paths for use in practice. Theoretical and empirical results both demonstrate that our proposed methodology breaks previously-established upper performance limits for traditional paths.
Parallel tempering (PT) methods are a popular class of Markov chain Monte Carlo schemes used to sample complex high-dimensional probability distributions. They rely on a collection of $N$ interacting auxiliary chains targeting temper
Informed MCMC methods have been proposed as scalable solutions to Bayesian posterior computation on high-dimensional discrete state spaces. We study a class of MCMC schemes called informed importance tempering (IIT), which combine importance sampling
In the current work we present two generalizations of the Parallel Tempering algorithm, inspired by the so-called continuous-time Infinite Swapping algorithm. Such a method, found its origins in the molecular dynamics community, and can be understood
We review several parallel tempering schemes and examine their main ingredients for accuracy and efficiency. The present study covers two selection methods of temperatures and several choices for the exchange of replicas, including a recent novel all
We study the performance of QCD simulations with dynamical Wilson fermions by combining the Hybrid Monte Carlo algorithm with parallel tempering on $10^4$ and $12^4$ lattices. In order to compare tempered with standard simulations, covariance matrice