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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 \u03c0 with a density L with respect to a reference distribution \u03c00 and compute the normalizing constant \u222bLd\u03c00. A typical use case is when \u03c00 is a prior distribution, L a likelihood function and \u03c0 the corresponding posterior distribution.<\/jats:p>","DOI":"10.1111\/rssb.12464","type":"journal-article","created":{"date-parts":[[2021,12,3]],"date-time":"2021-12-03T08:14:12Z","timestamp":1638519252000},"page":"321-350","source":"Crossref","is-referenced-by-count":60,"title":["Non-Reversible Parallel Tempering: A Scalable Highly Parallel MCMC Scheme"],"prefix":"10.1093","volume":"84","author":[{"given":"Saifuddin","family":"Syed","sequence":"first","affiliation":[{"name":"University of British Columbia , Vancouver, British Columbia , Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexandre","family":"Bouchard-C\u00f4t\u00e9","sequence":"additional","affiliation":[{"name":"University of British Columbia , Vancouver, British Columbia , Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"George","family":"Deligiannidis","sequence":"additional","affiliation":[{"name":"University of Oxford , Oxford, Oxfordshire , UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arnaud","family":"Doucet","sequence":"additional","affiliation":[{"name":"University of Oxford , Oxford, Oxfordshire , UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2021,12,3]]},"reference":[{"key":"2023022408360338300_","first-page":"12","article-title":"First M87 event horizon telescope results. 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