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• W2944392378 abstract "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 tempered versions of the target distribution to improve the exploration of the state-space. We provide here a new perspective on these highly parallel algorithms and their tuning by identifying and formalizing a sharp divide in the behaviour and performance of reversible versus non-reversible PT schemes. We show theoretically and empirically that a class of non-reversible PT methods dominates its reversible counterparts and identify distinct scaling limits for the non-reversible and reversible schemes, the former being a piecewise-deterministic Markov process and the latter a diffusion. These results are exploited to identify the optimal annealing schedule for non-reversible PT and to develop an iterative scheme approximating this schedule. We provide a wide range of numerical examples supporting our theoretical and methodological contributions. The proposed methodology is applicable to sample from a distribution $pi$ with a density $L$ with respect to a reference distribution $pi_0$ and compute the normalizing constant. A typical use case is when $pi_0$ is a prior distribution, $L$ a likelihood function and $pi$ the corresponding posterior." @default.
• W2944392378 created "2019-05-16" @default.
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• W2944392378 date "2019-05-08" @default.
• W2944392378 modified "2023-09-24" @default.
• W2944392378 title "Non-Reversible Parallel Tempering: an Embarassingly Parallel MCMC Scheme" @default.
• W2944392378 hasPublicationYear "2019" @default.
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