Tutorial on logistic-regression calibration and fusion: Converting a score to a likelihood ratio

TL;DR

This paper provides a practical tutorial on how logistic regression can calibrate and fuse scores from forensic systems to produce interpretable likelihood ratios, with applications beyond voice comparison.

Contribution

It offers a minimal-mathematical explanation of logistic-regression calibration and fusion for converting scores into likelihood ratios in forensic science.

Findings

Logistic regression effectively converts scores to likelihood ratios.

Calibration improves interpretability of scores in forensic analysis.

Fusion combines multiple scores to enhance decision accuracy.

Abstract

Logistic-regression calibration and fusion are potential steps in the calculation of forensic likelihood ratios. The present paper provides a tutorial on logistic-regression calibration and fusion at a practical conceptual level with minimal mathematical complexity. A score is log-likelihood-ratio like in that it indicates the degree of similarity of a pair of samples while taking into consideration their typicality with respect to a model of the relevant population. A higher-valued score provides more support for the same-origin hypothesis over the different-origin hypothesis than does a lower-valued score; however, the absolute values of scores are not interpretable as log likelihood ratios. Logistic-regression calibration is a procedure for converting scores to log likelihood ratios, and logistic-regression fusion is a procedure for converting parallel sets of scores from multiple forensic-comparison systems to log likelihood ratios. Logistic-regression calibration and fusion were developed for automatic speaker recognition and are popular in forensic voice comparison. They can also be applied in other branches of forensic science, a fingerprint/fingermark example is provided.