Non-Reversible Parallel Tempering: A Scalable Highly Parallel MCMC Scheme
Open accessAbstract
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 π with a density L with respect to a reference distribution π0 and compute the normalizing constant ∫Ldπ0. A typical use case is when π0 is a prior distribution, L a likelihood function and π the corresponding posterior distribution.
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Message passing variational autoregressive network for solving intractable Ising models
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Improved estimation of relaxation time in nonreversible Markov chains
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Control of probability flow in Markov chain Monte Carlo—Nonreversibility and lifting
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All in the Exponential Family: Bregman Duality in Thermodynamic Variational InferencePreprint
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Enhancing torsional sampling using fully adaptive simulated tempering
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Phase Diagram of Extensive-Rank Symmetric Matrix Denoising beyond Rotational Invariance
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An asymptotic Peskun ordering and its application to lifted samplers
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Origin of the ring ellipticity in the black hole images of M87 *
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Bayesian model inference with complex posteriors: Exponential-impact-informed Bayesian Quadrature
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A Continuation Method in Bayesian Inference
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Skew brownian motion and complexity of the alps algorithm
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Finite sample complexity of sequential Monte Carlo estimators on multimodal target distributions
Mathews, J., & Schmidler, S. C. (2024) · The Annals of Applied Probability · doi:10.1214/23-aap1989 · Cited by 4 · see citing works
Parallel Tempering on Optimized PathsPreprint
Syed, S., Romaniello, V., Campbell, T., & Bouchard‐Côté, A. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2102.07720 · Cited by 4 · see citing works
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Bayesian Constraints on the Ring Ellipticity of M87* 2017 Using Themis
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On the Orbit of the Binary Brown Dwarf Companion GL229 Ba and Bb
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Hamiltonian Assisted Metropolis SamplingPreprint
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Automatic Regenerative Simulation via Non-Reversible Simulated Tempering
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Quantum-inspired tempering for ground state approximation using artificial neural networks
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Noise-robust analysis of X-Ray absorption near-edge structure based on poisson distribution
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Bionic fractionalization in the trimer model of twisted bilayer graphene
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A connection between Tempering and Entropic Mirror DescentPreprint
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Non-reversible Parallel Tempering for Deep Posterior Approximation
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Theoretical guarantees for lifted samplers
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An embedded diachronic sense change model with a case study from ancient Greek
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Online updating estimation for streaming survival datasets
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An Ethnomathematics Approach to the Haida Stick Game
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Multiscale Parallel Tempering for Fast Sampling on Redistricting Plans
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FEAT: Free energy Estimators with Adaptive Transport *
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Optimized annealed sequential Monte Carlo samplers
Syed, S., Bouchard‐Côté, A., Chern, K. T., & Arnaud Doucet, B. (2026) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1093/jrsssb/qkag082
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- Authors
- Syed, S., Bouchard-Côté, A., Deligiannidis, G., & Doucet, A.
- Affiliations
- University of British Columbia (CA)
- University of British Columbia , Vancouver, British Columbia , Canada
- University of Oxford (GB)
- University of Oxford , Oxford, Oxfordshire , UK
- Corresponding author
- Syed, Saifuddin
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 2021-12-03
- Volume
- 84
- Issue
- 2
- Pages
- 321-350
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W2977245197
- Cited by
- 68
- References
- 95
- Citations by year
- 2026: 9 · 2025: 20 · 2024: 16 · 2023: 8 · 2022: 6 · 2021: 4 · 2020: 5
- FWCI
- 6.35
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)
- Locations
- Journal of the Royal Statistical Society Series B (Statistical Methodology) (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Engineering and Physical Sciences Research Council (EP/R034710/1, EP/R018561/1)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Simulation Techniques and Applications
- Keywords
- parallel tempering, non-reversible Markov chains, reversible Markov chains, Markov chain Monte Carlo, annealing schedule, piecewise deterministic Markov processes, diffusion approximation, scaling limits, posterior sampling, high-dimensional sampling
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