Normalisation-Based Likelihood Ratio Estimation for Forensic Authorship Verification

2026-07-10

AI Summary

This study addresses the limitations of traditional score-based approaches in forensic authorship verification, which rely on separate calibration models to produce reliable likelihood ratios—requiring extensive data and complex procedures. The authors propose two normalization methods, square-root correction and Hapax correction, that directly estimate well-calibrated likelihood ratios from LambdaG outputs without any external calibration. This work presents the first approach capable of generating properly calibrated likelihood ratios in a calibration-free manner, effectively mitigating the overestimation of evidential strength caused by long or highly repetitive texts. Experimental results across 15 corpora demonstrate that the proposed methods perform comparably to logistic regression calibration, with Hapax correction outperforming it in approximately 45% of scenarios and exhibiting smaller performance gaps when inferior, thereby substantially reducing data requirements and operational complexity.

Abstract

Authorship verification (AV) is the task of determining whether two texts were written by the same author. In a forensic context, the strength of AV evidence can be quantified using likelihood ratios. Most AV methods are score-based and deriving well-calibrated likelihood ratios from these scores requires a separate calibration model. This, in turn, requires additional amounts of case-relevant data, which is often time-consuming to obtain and prepare. This study proposes two novel normalisation techniques, the Square Root Correction and the Hapax Correction, for deriving likelihood ratios from the AV method LambdaG without the need of a calibration model (Nini et al. 2026). These corrections are designed to mitigate the overestimation of evidential strength that may result from long or highly repetitive texts. Performance is evaluated against logistic regression calibration across fifteen corpora and a range of text lengths (100-9,500 tokens), using the log-likelihood ratio cost (Cllr). The proposed methods achieve performance comparable to logistic regression calibration, with the Hapax Correction outperforming it in approximately 45% of tests (weighted by corpora). Furthermore, performance was more frequently close (within 5%) when the Hapax Correction was outperformed by logistic regression calibration, compared with the reverse comparison. Eliminating the need to train a calibration model reduces data-requirements, time and complexity, thereby increasing the accessibility and transparency of forensic text comparison. This combination of empirical performance and practical advantages supports the adoption of the proposed methods in forensic settings.

Problem

• authorship verification
• likelihood ratio
• calibration
• forensic linguistics
• text comparison

Innovation

• normalisation-based likelihood ratio
• authorship verification
• calibration-free
• Hapax Correction
• forensic text comparison