# Calibrating generalized predictive distributions

arXiv: https://arxiv.org/abs/2107.01688 · HTML: https://mlsanity.com/paper/2107.01688/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2021.

## Built on by (most cited first, 3 of 3)

- [Scalable Semi-Modular Inference with Variational Meta-Posteriors](https://mlsanity.com/paper/2204.00296/) (2022)
- [Temperature Optimization for Bayesian Deep Learning](https://mlsanity.com/paper/2410.05757/) (2024)
- [Maximin Robust Bayesian Experimental Design](https://mlsanity.com/paper/2603.14094/) (2026)

## Abstract (arXiv)

In prediction problems, it is common to model the data-generating process and then use a model-based procedure, such as a Bayesian predictive distribution, to quantify uncertainty about the next observation. However, if the posited model is misspecified, then its predictions may not be calibrated -- that is, the predictive distribution's quantiles may not be nominal frequentist prediction upper limits, even asymptotically. Rather than abandoning the comfort of a model-based formulation for a more complicated non-model-based approach, here we propose a strategy in which the data itself helps determine if the assumed model-based solution should be adjusted to account for model misspecification. This is achieved through a generalized Bayes formulation where a learning rate parameter is tuned, via the proposed generalized predictive calibration (GPrC) algorithm, to make the predictive distribution calibrated, even under model misspecification. Extensive numerical experiments are presented, under a variety of settings, demonstrating the proposed GPrC algorithm's validity, efficiency, and robustness.