Flexible Transformations for Bayesian Score Calibration
Abstract
Modern statistical models are growing increasingly complex in an effort to realistically capture system dynamics. Using standard simulation-based inference, these models may be computationally prohibitive, necessitating the use of model calibration methods. Bayesian score calibration is a computationally efficient framework for model calibration with strong theoretical guarantees. This framework learns an appropriate correction for an approximate model using a small number of simulations from the data-generating process. Currently, only a location-scale transformation has been explored, which may lack the flexibility to correct the complex error introduced by some approximate models. In this paper, we develop two flexible transformations for use in the Bayesian score calibration framework. The first is a polynomial extension, which can appropriately adjust approximate models with location-varying error. The second is a sequential application of Bayesian score calibration, which can accommodate approximate models with posteriors that have low support for the true parameter values. We also discuss an additional diagnostic for use with this framework. We demonstrate the increased flexibility these two approaches provide over Bayesian score calibration in two illustrative simulation studies.
Related
- Conformalized Quantile Regression and Minimax Limits of Fixed-Score Calibration under Known Covariate Shift
- Rényi-Regularized Flow-Based Variational Inference for Bayesian Calibration
- Posterior Geometry and Identifiability in Multi-Response Bayesian Calibration
- Calibration-Free Robust Bayesian Inference for Discrete Unnormalized Models
- Goal-Oriented Lower-Tail Calibration of Gaussian Processes for Bayesian Optimization
BibTeX
@misc{bretherton2026flexible,
title = {{Flexible Transformations for Bayesian Score Calibration}},
author = {Adam Bretherton and Joshua J. Bon and David J. Warne and David J. Nott and Christopher Drovandi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05772},
eprint = {2609.05772},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05772},
}
RIS
TY - UNPB
TI - Flexible Transformations for Bayesian Score Calibration
AU - Adam Bretherton
AU - Joshua J. Bon
AU - David J. Warne
AU - David J. Nott
AU - Christopher Drovandi
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.05772
UR - https://arxiv.org/abs/2609.05772
AB - Modern statistical models are growing increasingly complex in an effort to realistically capture system dynamics. Using standard simulation-based inference, these models may be computationally prohibitive, necessitating the use of model calibration methods. Bayesian score calibration is a computationally efficient framework for model calibration with strong theoretical guarantees. This framework learns an appropriate correction for an approximate model using a small number of simulations from the data-generating process. Currently, only a location-scale transformation has been explored, which may lack the flexibility to correct the complex error introduced by some approximate models. In this paper, we develop two flexible transformations for use in the Bayesian score calibration framework. The first is a polynomial extension, which can appropriately adjust approximate models with location-varying error. The second is a sequential application of Bayesian score calibration, which can accommodate approximate models with posteriors that have low support for the true parameter values. We also discuss an additional diagnostic for use with this framework. We demonstrate the increased flexibility these two approaches provide over Bayesian score calibration in two illustrative simulation studies.
ER -