Calibration-Free Robust Bayesian Inference for Discrete Unnormalized Models
Abstract
Bayesian inference for discrete models with intractable normalizing constants is computationally challenging, particularly when the sample space is large or countably infinite. Although some likelihood-based Bayesian methods can circumvent the intractable normalizing constant, their uncertainty quantification may be poorly calibrated under model misspecification. Generalized Bayesian approaches can address this calibration issue, but typically require careful tuning of a learning rate. In this paper, we propose DFD-BETEL, a semiparametric Bayesian framework that uses the first-order optimality conditions of discrete Fisher divergence as moment conditions in Bayesian exponentially tilted empirical likelihood. The resulting posterior avoids evaluation of the normalizing constant and requires no learning-rate calibration. We establish consistency and asymptotic normality of the discrete Fisher divergence estimator and prove a Bernstein-von Mises theorem for the DFD-BETEL posterior, showing that its limiting covariance matches the sampling covariance of the estimator and yields asymptotically calibrated uncertainty quantification. Numerical studies show that DFD-BETEL remains competitive with likelihood-based Bayesian inference under correct specification and provides more reliable uncertainty quantification under model misspecification. An application to automobile-insurance claim data further illustrates the practical utility of DFD-BETEL.
Related
- Robust Bayesian Inference for Unnormalized Models with Mixed-Domain Data
- Rényi-Regularized Flow-Based Variational Inference for Bayesian Calibration
- Concentration and Calibration in Predictive Bayesian Inference
- Parameter Estimation for Unnormalized Discrete Models via Empirically Localized Deformed Bregman Divergence
- Coherent and robust Bayesian inference under informative sampling via sample-level weight models
BibTeX
@misc{wang2026calibrationfree,
title = {{Calibration-Free Robust Bayesian Inference for Discrete Unnormalized Models}},
author = {Jiongran Wang and Debdeep Pati and Anirban Bhattacharya},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09214},
eprint = {2610.09214},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09214},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Calibration-Free Robust Bayesian Inference for Discrete Unnormalized Models
AU - Jiongran Wang
AU - Debdeep Pati
AU - Anirban Bhattacharya
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.09214
UR - https://arxiv.org/abs/2610.09214
AB - Bayesian inference for discrete models with intractable normalizing constants is computationally challenging, particularly when the sample space is large or countably infinite. Although some likelihood-based Bayesian methods can circumvent the intractable normalizing constant, their uncertainty quantification may be poorly calibrated under model misspecification. Generalized Bayesian approaches can address this calibration issue, but typically require careful tuning of a learning rate. In this paper, we propose DFD-BETEL, a semiparametric Bayesian framework that uses the first-order optimality conditions of discrete Fisher divergence as moment conditions in Bayesian exponentially tilted empirical likelihood. The resulting posterior avoids evaluation of the normalizing constant and requires no learning-rate calibration. We establish consistency and asymptotic normality of the discrete Fisher divergence estimator and prove a Bernstein-von Mises theorem for the DFD-BETEL posterior, showing that its limiting covariance matches the sampling covariance of the estimator and yields asymptotically calibrated uncertainty quantification. Numerical studies show that DFD-BETEL remains competitive with likelihood-based Bayesian inference under correct specification and provides more reliable uncertainty quantification under model misspecification. An application to automobile-insurance claim data further illustrates the practical utility of DFD-BETEL.
ER -