mlsanityData to 7 Oct 2026

Rank-normalization, folding, and localization: An improved widehatR for assessing convergence of MCMC

arXiv 1903.08008 ↗First posted 19 Mar 2019stat.CO stat.MEcited by 90

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Abstract (arXiv)

Markov chain Monte Carlo is a key computational tool in Bayesian statistics, but it can be challenging to monitor the convergence of an iterative stochastic algorithm. In this paper we show that the convergence diagnostic widehatR of Gelman and Rubin (1992) has serious flaws. Traditional widehatR will fail to correctly diagnose convergence failures when the chain has a heavy tail or when the variance varies across the chains. In this paper we propose an alternative rank-based diagnostic that fixes these problems. We also introduce a collection of quantile-based local efficiency measures, along with a practical approach for computing Monte Carlo error estimates for quantiles. We suggest that common trace plots should be replaced with rank plots from multiple chains. Finally, we give recommendations for how these methods should be used in practice.

Key facts. Cited by 90 papers in the map (data through 7 Oct 2026). First posted on arXiv 19 Mar 2019.

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Citing papers per year: 2021: 7; 2022: 9; 2023: 20; 2024: 16; 2025: 15; 2026: 23.

90 papers.

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  1. 2021Bayesian Neural Network Priors Revisitedcited by 121
  2. 2021Pathfinder: Parallel quasi-Newton variational inferencecited by 26
  3. 2023A Primer on Bayesian Neural Networks: Review and Debatescited by 26
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  8. 2025Microcanonical Langevin Ensembles: Advancing the Sampling of Bayesian Neural Networkscited by 10
  9. 2023Misspecification-robust Sequential Neural Likelihood for Simulation-based Inferencecited by 8
  10. 2023Bayesian neural networks via MCMC: a Python-based tutorialcited by 8
  11. 2023On the Properties and Estimation of Pointwise Mutual Information Profilescited by 7
  12. 2023Bayesian Hierarchical Models for Counterfactual Estimationcited by 6
38 more
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  5. 2021Entropy-based adaptive Hamiltonian Monte Carlocited by 5
  6. 2021Bounding Wasserstein distance with couplingscited by 5
  7. 2022Scalable Spike-and-Slabcited by 5
  8. 2022A fully Bayesian sparse polynomial chaos expansion approach with joint priors on the coefficients and global selection of termscited by 5
  9. 2023Coreset Markov Chain Monte Carlocited by 5
  10. 2024Listening to the Noise: Blind Denoising with Gibbs Diffusioncited by 5
  11. 2024Network reconstruction via the minimum description length principlecited by 5
  12. 2024Approximately-symmetric neural networks for quantum spin liquidscited by 5
  13. 2024Simulation-based Inference with the Python Package sbijaxcited by 5
  14. 2025RefineStat: Efficient Exploration for Probabilistic Program Synthesiscited by 5
  15. 2022Sparse Gaussian Process Hyperparameters: Optimize or Integrate?cited by 4
  16. 2023Balanced Training of Energy-Based Models with Adaptive Flow Samplingcited by 4
  17. 2023Uncertainty Quantification and Propagation in Surrogate-based Bayesian Inferencecited by 4
  18. 2024Tuning diagonal scale matrices for HMCcited by 4
  19. 2024RiskLabs: Predicting Financial Risk Using Large Language Model based on Multimodal and Multi-Sources Datacited by 4
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  22. 2025Posterior SBC: Simulation-Based Calibration Checking Conditional on Datacited by 3
  23. 2025A Langevin sampling algorithm inspired by the Adam optimizercited by 3
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  26. 2025Benchmarking Diffusion Annealing-Based Bayesian Inverse Problem Solverscited by 2
  27. 2022Bayesian NVH metamodels to assess interior cabin noise using measurement databasescited by 1
  28. 2022Bayesian nonparametric mixture inconsistency for the number of components: How worried should we be in practice?cited by 1
  29. 2023An Interpretable Determinantal Choice Model for Subset Selectioncited by 1
  30. 2023A Targeted Accuracy Diagnostic for Variational Approximationscited by 1
  31. 2024Fast Bayesian Inference for Neutrino Non-Standard Interactions at Dark Matter Direct Detection Experimentscited by 1
  32. 2024Symmetry-driven embedding of networks in hyperbolic spacecited by 1
  33. 2024Multitask learning for improved scour detection: A dynamic wave tank studycited by 1
  34. 2024Temperature Optimization for Bayesian Deep Learningcited by 1
  35. 2024ELBOing Stein: Variational Bayes with Stein Mixture Inferencecited by 1
  36. 2025CoCoAFusE: Beyond Mixtures of Experts via Model Fusioncited by 1
  37. 2025Uncertainty-Aware Surrogate-based Amortized Bayesian Inference for Computationally Expensive Modelscited by 1
  38. 2026LLM surprisal is necessary but not sufficient to capture English garden-path effects: Evidence from joint latent modeling of reading paradigmscited by 1

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