mlsanityData to 7 Oct 2026

General Bayesian Updating and the Loss-Likelihood Bootstrap

arXiv 1709.07616 ↗First posted 22 Sep 2017stat.ME stat.MLcited by 34

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Abstract (arXiv)

In this paper we revisit the weighted likelihood bootstrap, a method that generates samples from an approximate Bayesian posterior of a parametric model. We show that the same method can be derived, without approximation, under a Bayesian nonparametric model with the parameter of interest defined as minimising an expected negative log-likelihood under an unknown sampling distribution. This interpretation enables us to extend the weighted likelihood bootstrap to posterior sampling for parameters minimizing an expected loss. We call this method the loss-likelihood bootstrap. We make a connection between this and general Bayesian updating, which is a way of updating prior belief distributions without needing to construct a global probability model, yet requires the calibration of two forms of loss function. The loss-likelihood bootstrap is used to calibrate the general Bayesian posterior by matching asymptotic Fisher information. We demonstrate the methodology on a number of examples.

Key facts. Cited by 34 papers in the map (data through 7 Oct 2026). First posted on arXiv 22 Sep 2017.

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Citing papers per year: 2021: 3; 2022: 2; 2023: 8; 2024: 8; 2025: 3; 2026: 10.

34 papers.

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  1. 2021Robust Generalised Bayesian Inference for Intractable Likelihoodscited by 53
  2. 2022Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrapcited by 41
  3. 2023Robust and Scalable Bayesian Online Changepoint Detectioncited by 16
  4. 2022Generalised Bayesian Inference for Discrete Intractable Likelihoodcited by 14
  5. 2023Robust and Conjugate Gaussian Process Regressioncited by 14
  6. 2024Sourcerer: Sample-based Maximum Entropy Source Distribution Estimationcited by 9
  7. 2024Concentration of a sparse Bayesian model with Horseshoe prior in estimating high-dimensional precision matrixcited by 8
  8. 2024Concentration properties of fractional posterior in 1-bit matrix completioncited by 7
  9. 2024A sparse PAC-Bayesian approach for high-dimensional quantile predictioncited by 6
  10. 2025AI-Powered Bayesian Inferencecited by 6
  11. 2024Enhancing Transfer Learning with Flexible Nonparametric Posterior Samplingcited by 5
  12. 2021Mitigating Statistical Bias within Differentially Private Synthetic Datacited by 4
22 more
  1. 2023Semiparametric inference using fractional posteriorscited by 4
  2. 2023A Semi-Bayesian Nonparametric Estimator of the Maximum Mean Discrepancy Measure: Applications in Goodness-of-Fit Testing and Generative Adversarial Networkscited by 3
  3. 2023Robust Bayesian Inference for Measurement Error Misspecification: The Berkson and Classical Casescited by 2
  4. 2023Reproducible Parameter Inference Using Bagged Posteriorscited by 2
  5. 2024Interventional Processes for Causal Uncertainty Quantificationcited by 2
  6. 2023A Bayesian Non-parametric Approach to Generative Models: Integrating Variational Autoencoder and Generative Adversarial Networks using Wasserstein and Maximum Mean Discrepancycited by 1
  7. 2023Sequential Gibbs Posteriors with Applications to Principal Component Analysiscited by 1
  8. 2024Adaptive posterior concentration rates for sparse high-dimensional linear regression with random design and unknown error variancecited by 1
  9. 2024Temperature Optimization for Bayesian Deep Learningcited by 1
  10. 2026Amortized Simulation-Based Inference in Generalized Bayes via Neural Posterior Estimationcited by 1
  11. 2026Generalised Robust Bayes for Joint Inference of Model and Contaminationcited by 1
  12. 2021Nonparametric posterior learning for emission tomography with multimodal datacited by 0
  13. 2025A Deep Bayesian Nonparametric Framework for Robust Mutual Information Estimationcited by 0
  14. 2025A weighted-likelihood framework for class imbalance in Bayesian prediction modelscited by 0
  15. 2026When Is Generalized Bayes Bayesian? A Decision-Theoretic Characterization of Loss-Based Updatingcited by 0
  16. 2026General Bayesian Policy Learningcited by 0
  17. 2026Bayesian X-Learner: Calibrated Posterior Inference for Heterogeneous Treatment Effects under Heavy-Tailed Outcomescited by 0
  18. 2026Supercharging Bayesian Inference with Reliable AI-Informed Priorscited by 0
  19. 2026Variational predictive resamplingcited by 0
  20. 2026Calibrated Inference for the Conditional Average Treatment Effect in the Few-Placebo Regime via Gaussian Processescited by 0
  21. 2026Dirichlet Follow-the-Leader Closes the Gap in Simultaneous Multiclass U-Calibrationcited by 0
  22. 2026Bootstrap validity in Bayesian semi-parametric modelscited by 0