Markov Chain Monte Carlo

Also known as MCMC

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Overview

Markov Chain Monte Carlo (MCMC) generates dependent samples from complex distributions, making it useful for Bayesian inference, uncertainty quantification, and physical simulations where direct sampling is difficult. Core methods include Metropolis–Hastings and Gibbs sampling, gradient-based Langevin and Hamiltonian Monte Carlo, and non-reversible samplers; tempering and sequential Monte Carlo are often combined with them to explore multiple modes. Current work also uses learned proposals, normalizing flows, and diffusion models to improve exploration, while acceptance corrections can preserve the target distribution. A central tension is achieving reliable convergence and accurate uncertainty estimates at manageable computational cost, especially for high-dimensional or multimodal targets where chains can mix slowly and diagnostics may be inconclusive.

Latest papers

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150 papers21 papers in the last four weeks, down 16% on the four weeks before. 0.1% of all new papers.

  1. Foresight: Learning Twisted SMC for Rare Events from Reversed Relaxations

    Oct 31, 2026Ziyi Fan, Yuxuan Qiu, Haibo Wang +2Rare-Event EstimationMarkov Chain Monte Carlo

    Key Laboratory of Organ Regeneration and Reconstruction, Chinese Academy of Sciences, Beijing, China · Institute of Industrial Science, The University of Tokyo, Tokyo, Japan · Westlake University, Hangzhou, China +1

  2. Averaged Annealed Markov Chains Achieve the Algorithmic Threshold for Tensor PCA, Part II: Langevin Dynamics

    Oct 28, 2026Aniket Das, Tselil SchrammTensor DecompositionLangevin Dynamics

    Stanford University

  3. Underdamped Anchored Langevin Dynamics

    Oct 27, 2026Qi Feng, Hoang M. Nguyen, Lingjiong ZhuMarkov Chain Monte CarloLangevin Dynamics

    Department of Mathematics, Florida State University, 1017 Academic Way, Tallahassee, FL-32306, United States of America

  4. Generalizing Metropolis-Hastings for DAG Sampling

    Oct 21, 2026Daniele Nikzad, Mikko KoivistoBayesian Network Structure LearningMarkov Chain Monte Carlo

    Department of Computer Science, University of Helsinki, Helsinki, FI-00014, Finland

  5. Decoupled Marginal Sharpening for Training-Free Inference-Time Scaling

    Oct 14, 2026Weixin Wang, Wei Deng, Anderson Schneider +3Inference-Time ScalingEfficient Language Model Reasoning

    Duke University · Morgan Stanley

  6. Learning Graph Energies for Finite-Time Generation

    Oct 14, 2026Amartya Banerjee, Xingyu Xu, Caroline Moosmüller +1Energy-Based ModelsMolecular Graph Generation

  7. Theoretical and Practical Advances in Hierarchical Bayesian Deep Learning Methodology

    Oct 13, 2026Neil K. Chada, Simon Cotter, Kody J. H. Law +1Bayesian Neural NetworksHierarchical Bayesian Modeling

    Department of Mathematics, City University of Hong Kong, Hong Kong SAR. · School of Mathematics, University of Manchester, UK.

  8. BridgeTwist: Twisting Schrödinger Bridges for Training-Free Conditional Sampling

    Oct 13, 2026Mengyu Li, Qianqian Qu, Jun S. LiuConditional Generative ModelingPosterior Sampling

    Department of Statistics and Data Science, Tsinghua University, Beijing, China

  9. SCOPE Before You Sample: Conformal Scores Guide Posterior Exploration for Fast and Calibrated Bayesian Predictive Inference

    Oct 12, 2026Zahra Moslemi, Ziyi Liang, Babak ShahbabaBayesian InferencePosterior Sampling

    University of California, Irvine · University of California, Santa Barbara

  10. NFDiag\texttt{NFDiag}: High-dimensional MCMC Convergence Diagnosis with Normalizing Flows

    Oct 12, 2026Kutay Nazlı, Elena SellentinMarkov Chain Monte CarloBayesian Inference

    Leiden Observatory, Leiden University, Einsteinweg 55 2333 CC Leiden, Netherlands · Mathematical Institute, Leiden University, Einsteinweg 55 2333 CC Leiden, Netherlands

  11. Sampling from Neural Operator Priors to Solve Partial Differential Equations

    Oct 12, 2026Andrew Millard, Joshua Murphy, Zheng ZhaoPDE SolvingPartial Differential Equations

    Department of Computer and Information Science, Linköping University, Sweden. · Department of Political Science, Trinity College Dublin, Ireland.

  12. Inference-Time Steering Across Scaffolds and Epitopes for Sample-Efficient De Novo Nanobody Design

    Oct 9, 2026Mason Minot, Simon Friedensohn, Cédric R. WeberInference-Time Compute AllocationProtein Binder Design

    Alloy Therapeutics Allschwil, Switzerland

  13. PreSTO: Predictive Subtree Prefetching for Fast LLM Power Sampling

    Oct 9, 2026Nan Jiang, Panagiotis Theodoropoulos, Wei DengLLM Inference AccelerationMarkov Chain Monte Carlo

    University of Texas at El Paso · Georgia Institute of Technology · Morgan Stanley

  14. Amortised Inference through One-Step Implicit Sampling

    Oct 8, 2026Vincent Pauline, Kirill Tamogashev, Arran Carter +3Amortized InferencePosterior Sampling

    Technical University of Munich · Munich Center for Machine Learning · University of Edinburgh +1

  15. Accelerating Non-Smooth and Heavy-Tailed Sampling

    Oct 8, 2026Pervez Ali, Xiaoyu Wang, Yingli Wang +1Constrained SamplingLangevin Dynamics

    Department of Mathematics, Florida State University, Tallahassee, Florida, United States of America · Fintech Thrust, Hong Kong University of Science and Technology (Guangzhou), Guangzhou, Guangdong Province, People’s Republic of China · School of Mathematical Sciences, Fudan University, Shanghai, People’s Republic of China

  16. Transformed Samplers with Variance Reduction

    Oct 7, 2026Siran Liu, Michalis Tisias, Petros DellaportasMarkov Chain Monte CarloVariance Reduction

    Department of Statistical Science, University College London, UK. · Google DeepMind, UK. · Department of Statistical Science, University College London, UK, and Department of Statistics, Athens University of Economics and Business, Greece.

  17. Broadly Applicable Approximate MCMC for Switching Stochastic Differential Equations Using Uniformization and Time-Conditioned Factorized Neural Likelihood Estimation

    Oct 7, 2026Shion Hosoda, Michiaki HamadaStochastic Differential EquationsRegime-Switching Dynamical Systems

    Waseda University · National Institute of Advanced Industrial Science and Technology · Nippon Medical School

  18. Kinetic Langevin Meets Split Gibbs: Accelerated Posterior Sampling for Imaging Inverse Problems with Diffusion Priors

    Oct 7, 2026Dai Hai Nguyen, Duc Dung NguyenBayesian Inverse ProblemsMarkov Chain Monte Carlo

    Hokkaido University · Institute of Information Technology, VAST

  19. Reflected Anchored Langevin Algorithms

    Oct 7, 2026Changwei Tu, Xiaoyu Wang, Yingli Wang +2Constrained SamplingLangevin Dynamics

    Hong Kong University of Science and Technology (Guangzhou), Guangzhou, Guangdong Province, People’s Republic of China · School of Mathematical Sciences, Fudan University, Shanghai, People’s Republic of China · School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, People’s Republic of China +1

  20. Noise, Denoise, Correct: MCMC Posterior Sampling with Diffusion Priors in Three Steps

    Oct 7, 2026So Takao, Gregory David Bellchambers, Luke Ye +2Diffusion Posterior SamplingDiffusion-Based Inverse Problems

    PhysicsX London, UK

  21. Sharp dimensional analysis of midpoint methods for Langevin sampling

    Oct 5, 2026Fan Chen, Sinho Chewi, Jianfeng Lu +1Markov Chain Monte CarloStochastic Differential Equations

    Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology. · Department of Statistics and Data Science, Yale University. · Department of Mathematics, Duke University. +1

  22. Gradient-Free Sampling from Generative Models via Stochastic Bounded Extremum Seeking

    Oct 3, 2026Alexander ScheinkerDiffusion SamplingMarkov Chain Monte Carlo

    Instrumentation and Controls Group Los Alamos National Laboratory Los Alamos, NM 87544, USA

  23. Metropolis-Hastings Dominates Importance Resampling for Policy Composition

    Oct 2, 2026Alexey Kurennoy, Ramil Yarullin, Fergal ReidIndependent Metropolis-HastingsLanguage Model Decoding

  24. LatticeSMC: Where to Spend Inference-Time Compute in Chunked Sequence Generators

    Oct 2, 2026Xuanchen Wang, Heng Wang, Weidong CaiInference-Time GuidanceDiffusion Model Sampling

    School of Computer Science The University of Sydney Sydney, NSW, Australia

  25. ENCORE: Exact Non-equilibrium COntrol with Replica Exchange for Diffusion Generation

    Oct 1, 2026Jiahao Yu, Saifuddin Syed, José Miguel Hernández-Lobato +1Inference-Time GuidanceDiffusion Sampling

    University of Oxford · University of Cambridge · University of British Columbia

  26. Muon meets Tamed Langevin: Momentum Preconditioning beyond Convex and gradient-Lipschitz Potentials

    Oct 1, 2026Nikolaos Makras, Sotirios SabanisMarkov Chain Monte CarloMomentum Methods

    School of Mathematics, University of Edinburgh, UK · National Technical University of Athens, Greece · Athena/Archimedes Research Centre, Greece

  27. Error-Corrected Inference-Time Scaling for Imperfect Diffusion Models

    Oct 1, 2026Zuokai Wen, Louis Grenioux, Weinan E +1Markov Chain Monte CarloDiffusion Model Sampling

    School of Artificial Intelligence, Shanghai Jiao Tong University · Center for Computational Mathematics, Flatiron Institute · School of Mathematical Sciences, Peking University

  28. Posterior sampling by source-space MCMC via prior-based few-step transport maps

    Oct 1, 2026Hoang Phuc Hau Luu, Marcelo Hartmann, Zhongjian WangMarkov Chain Monte CarloBayesian Inference

    Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore. · Department of Computer Science, Faculty of Science, University of Helsinki, Finland.

  29. Near-Linear Accuracy Bounds for Moreau--Yosida Unadjusted Langevin Sampling

    Sep 30, 2026Yuchen Xin, Zhihua ZhangMarkov Chain Monte CarloLangevin Dynamics

    School of Mathematical Sciences, Peking University

  30. Iterative Exact Discrete Guidance for Energy-Based Sampling

    Sep 29, 2026Yuwen Qian, Yidong Ouyang, Zhengyan Wan +1Sampling from Unnormalized DistributionsAdaptive Sampling

    School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen · Department of Statistics, University of California, Los Angeles · School of Data Science, The Chinese University of Hong Kong, Shenzhen