mlsanityData to 7 Oct 2026

Marginal likelihood computation for model selection and hypothesis testing: an extensive review

arXiv 2005.08334 ↗First posted 17 May 2020stat.CO cs.LGcited by 33

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Abstract (arXiv)

This is an up-to-date introduction to, and overview of, marginal likelihood computation for model selection and hypothesis testing. Computing normalizing constants of probability models (or ratio of constants) is a fundamental issue in many applications in statistics, applied mathematics, signal processing and machine learning. This article provides a comprehensive study of the state-of-the-art of the topic. We highlight limitations, benefits, connections and differences among the different techniques. Problems and possible solutions with the use of improper priors are also described. Some of the most relevant methodologies are compared through theoretical comparisons and numerical experiments.

Key facts. Cited by 33 papers in the map (data through 7 Oct 2026). First posted on arXiv 17 May 2020.

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Citing papers per year: 2021: 8; 2022: 6; 2023: 3; 2024: 4; 2025: 6; 2026: 6.

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  1. 2021Scalable Marginal Likelihood Estimation for Model Selection in Deep Learningcited by 105
  2. 2021Priors in Bayesian Deep Learning: A Reviewcited by 101
  3. 2021Annealed Flow Transport Monte Carlocited by 90
  4. 2022Bayesian Model Selection, the Marginal Likelihood, and Generalizationcited by 56
  5. 2024Liouville Flow Importance Samplercited by 25
  6. 2021BNNpriors: A library for Bayesian neural network inference with different prior distributionscited by 20
  7. 2021Revisiting Bayesian Autoencoders with MCMCcited by 10
  8. 2023Approximately Bayes-Optimal Pseudo Label Selectioncited by 10
  9. 2021A survey of Monte Carlo methods for noisy and costly densities with application to reinforcement learning and ABCcited by 8
  10. 2022Generalized Bayesian Additive Regression Trees Models: Beyond Conditional Conjugacycited by 8
  11. 2021Automatic tempered posterior distributions for Bayesian inversion problemscited by 6
  12. 2024Dynamic Online Ensembles of Basis Expansionscited by 5
21 more
  1. 2025Improving the Accuracy of Amortized Model Comparison with Self-Consistencycited by 5
  2. 2022On the safe use of prior densities for Bayesian model selectioncited by 4
  3. 2021MCMC-driven importance samplerscited by 3
  4. 2022Marginal and Joint Cross-Entropies & Predictives for Online Bayesian Inference, Active Learning, and Active Samplingcited by 3
  5. 2023Adaptive importance sampling for heavy-tailed distributions via α-divergence minimizationcited by 3
  6. 2022Optimality in Noisy Importance Samplingcited by 2
  7. 2023Spectral information criterion for automatic elbow detectioncited by 2
  8. 2025FlowVAT: Normalizing Flow Variational Inference with Affine-Invariant Temperingcited by 2
  9. 2022Inference over radiative transfer models using variational and expectation maximization methodscited by 1
  10. 2024Divide, Conquer, Combine Bayesian Decision Tree Samplingcited by 1
  11. 2024Variational Neural Stochastic Differential Equations with Change Pointscited by 1
  12. 2025Adaptive posterior distributions for uncertainty analysis of covariance matrices in Bayesian inversion problems for multioutput signalscited by 1
  13. 2025Fenchel-Young Variational Learningcited by 1
  14. 2025Enhancing Graphical Lasso: A Robust Scheme for Non-Stationary Mean Datacited by 1
  15. 2025On Equivariant Model Selection through the Lens of Uncertaintycited by 1
  16. 2026A note on the area under the likelihood and the fake evidence for model selectioncited by 0
  17. 2026Automatic Laplace Collapsed Sampling: Scalable Marginalisation of Latent Parameters via Automatic Differentiationcited by 0
  18. 2026A unifying view of contrastive learning, importance sampling, and bridge sampling for energy-based modelscited by 0
  19. 2026Self-Supervised Laplace Approximation for Bayesian Uncertainty Quantificationcited by 0
  20. 2026Nested Sampling: A Critical and Comprehensive Theoretical Guidecited by 0
  21. 2026Quenched Ensemble Samplingcited by 0