Calculation of Likelihood Ratios - Forensic Data Science Laboratory

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Home	Calculation of Likelihood Ratios

Calculation of likelihood ratios is also covered on other webpages within this website.
This page relates to reseach that does not fit into the topics of the other pages.

Selected Publications

Morrison G.S. (2025). Taking account of typicality in calculation of likelihood ratios. Law, Probabaility & Risk, 24, mgaf009.
https://doi.org/10.1093/lpr/mgaf009

Morrison G.S., Poh N. (2018). Avoiding overstating the strength of forensic evidence: Shrunk likelihood ratios / Bayes factors. Science & Justice, 58, 200–218.
https://doi.org/10.1016/j.scijus.2017.12.005

Morrison G.S., Enzinger E. (2018). Score based procedures for the calculation of forensic likelihood ratios – Scores should take account of both similarity and typicality. Science & Justice, 58, 47–58.
https://doi.org/10.1016/j.scijus.2017.06.005

Project:

Taking account of typicality in calculation of likelihood ratios

Publication:

Morrison G.S. (2024). Taking account of typicality in calculation of likelihood ratios. Law, Probabaility & Risk, 24, mgaf009. https://doi.org/10.1093/lpr/mgaf009

When calculating a likelihood ratio with respect to the question of whether two items originated from the same source or from different sources, one must take account of not only the similarity between the items but also their typicality with respect to the relevant population. Using simple univariate examples, this paper demonstrates that likelihood ratios calculated using specific-source and common-source methods do take account of typicality, but that likelihood ratios calculated from similarity scores do not. It also demonstrates that converting feature values to percentile-rank values before calculating similarity scores does not properly take account of typicality. The paper argues that methods that do not take account of typicality should not be used, and that methods that do take account of typicality should be used instead. Since sufficient case-relevant data to train a specific-known-source model are seldom available, the paper recommends that the method to use instead of the similarity-score method should usually be the common-source method.

Software and data:

Matlab code that runs the synthetic-data-based demonstrations and experiments described in the manuscript.

score_based_LRs_2025-07-04a.zip

Project:

Transforming DNN embeddings

Manuscript:

Ribeiro R.O., Weber P. Morrison G.S. (2026). Effects of applying Gaussianising transformations to DNN embeddings before calculating likelihood ratios. Manuscript submitted for publication.
Link to come

This paper investigates the effects of applying multiple different sequences of transformations that aim to Gaussianise the distribution of deep-neural-network embeddings (DNN embeddings) before those DNN embeddings are used to calculate likelihood ratios using a model that assumes Gaussian distributions (Probabilistic Linear Discriminant Analysis, PLDA). The transformations were originally developed for non-forensic applications of automatic speaker recognition. This paper investigates the effects of applying the transformations under three different sets of forensically realistic conditions. The paper assesses the effects of the transformations with respect to theoretical properties of high-dimensional Gaussian distributions, and with respect to their impact on the performance of a forensic-voice-comparison system. Considering both the distribution and the performance criteria, the sequence of transformations that appeared to give the best results was: linear discriminant functions + centring + whitening + radial Gaussianisation. The results are potentially generalisable and not just specific to forensic voice comparison, i.e., they are also potentially applicable to use of DNN embedding to calculate likelihood ratios in other branches of forensic science such as forensic comparison of facial images.

Software and data:

Python code and data.

Link to come