# Likelihood-ratio calibration using prior-weighted proper scoring rules

arXiv: https://arxiv.org/abs/1307.7981 · HTML: https://mlsanity.com/paper/1307.7981/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jul 2013.

## Built on by (most cited first, 4 of 4)

- [Analysis and Comparison of Classification Metrics](https://mlsanity.com/paper/2209.05355/) (2022)
- [A Speaker Verification Backend with Robust Performance across Conditions](https://mlsanity.com/paper/2102.01760/) (2021)
- [Investigation of Different Calibration Methods for Deep Speaker Embedding based Verification Systems](https://mlsanity.com/paper/2203.15106/) (2022)
- [Normalisation-Based Likelihood Ratio Estimation for Forensic Authorship Verification](https://mlsanity.com/paper/2607.09501/) (2026)

## Abstract (arXiv)

Prior-weighted logistic regression has become a standard tool for calibration in speaker recognition. Logistic regression is the optimization of the expected value of the logarithmic scoring rule. We generalize this via a parametric family of proper scoring rules. Our theoretical analysis shows how different members of this family induce different relative weightings over a spectrum of applications of which the decision thresholds range from low to high. Special attention is given to the interaction between prior weighting and proper scoring rule parameters. Experiments on NIST SRE'12 suggest that for applications with low false-alarm rate requirements, scoring rules tailored to emphasize higher score thresholds may give better accuracy than logistic regression.