Brier-UDAM for Paired Prediction-Rule Comparisons: Latent-Risk Interpretation, Observable Contrasts, and Inference

@misc{nakatani2026brierudam,
  title = {{Brier-UDAM for Paired Prediction-Rule Comparisons: Latent-Risk Interpretation, Observable Contrasts, and Inference}},
  author = {Eiji Nakatani and Hiroya Hashimoto},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.06945},
  eprint = {2609.06945},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06945},
}

TY  - UNPB
TI  - Brier-UDAM for Paired Prediction-Rule Comparisons: Latent-Risk Interpretation, Observable Contrasts, and Inference
AU  - Eiji Nakatani
AU  - Hiroya Hashimoto
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.06945
UR  - https://arxiv.org/abs/2609.06945
AB  - The Brier risk summarizes probability-prediction error but does not explain why two prediction rules differ. We develop Brier-UDAM, a framework for paired binary prediction-rule comparisons that separates the Brier-risk difference into mean-bias, dispersion, and Brier-scale alignment contributions. Although the observable contrast identity follows algebraically from Yates-type moment decompositions, the framework gives these terms a latent-risk interpretation and shows that paired contrasts can be identified from observed outcomes and paired predictions without estimating the conditional event-risk function. For two rules evaluated in the same target population, the exact identity ΔR = ΔM + ΔD + ΔL holds, and the corresponding plug-in estimators reproduce the empirical paired Brier-risk difference exactly in finite samples. We derive influence-function-based inference for first-order regular contrasts and a projection-based confidence procedure for the mean-bias contrast when first-order inference degenerates. Simulations confirmed interpretable component behavior, recovery of the target contrasts, and generally satisfactory inference in regular settings; projection intervals retained coverage near degeneracy but were conservative. In a large public-data analysis of 30-day hospital readmission, models with similar held-out Brier risks showed substantially larger and opposing dispersion and alignment contributions, revealing cancellation that was hidden in the aggregate score. Brier-UDAM therefore provides a diagnostic account of paired Brier-risk differences, while calibration, discrimination, and information-based assessments continue to address their distinct performance questions.
ER  -