Predictive Bayesian inference posteriors concentrate onto a forward-model-dependent quantity and produce miscalibrated credible sets unless the predictive model contains the true data-generating process.
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PAC-Bayes bounds for Gibbs posteriors are obtained via singular learning theory, producing explicit and tighter posterior-averaged risk bounds that adapt to data structure in overparameterized models.
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Concentration and Calibration in Predictive Bayesian Inference
Predictive Bayesian inference posteriors concentrate onto a forward-model-dependent quantity and produce miscalibrated credible sets unless the predictive model contains the true data-generating process.
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PAC-Bayes Bounds for Gibbs Posteriors via Singular Learning Theory
PAC-Bayes bounds for Gibbs posteriors are obtained via singular learning theory, producing explicit and tighter posterior-averaged risk bounds that adapt to data structure in overparameterized models.