Posterior distributions for likelihood ratios in forensic science

From data to a validated score-based LR system: A practitioner's guide

Likelihood ratios (LRs) are a useful measure of evidential strength. In forensic casework consisting of a flow of cases with essentially the same question and the same analysis method, it is feasible to construct an 'LR system', that is, an automated procedure that has the observations as input and an LR as output. This paper is aimed at practitioners interested in building their own LR systems. It gives an overview of the different steps needed to get to a validated LR system from data. The paper is accompanied by a notebook that illustrates each step with an example using glass data. The notebook introduces open-source software in Python constructed by NFI (Netherlands Forensic Institute) data scientists and statisticians.

A practical treatment of sensitivity analyses in activity level evaluations

Evaluations of forensic observations considering activity level propositions are becoming more common place in forensic institutions. A measure that can be taken to interrogate the evaluation for robustness is called sensitivity analysis. A sensitivity analysis explores the sensitivity of the evaluation to the data used when assigning probabilities, or to the level of uncertainty surrounding a probability assignment, or to the choice of various assumptions within the model. There have been a number of publications that describe sensitivity analysis in technical terms, and demonstrate their use, but limited literature on how that theory can be applied in practice. In this work we provide some simplified examples of how sensitivity analyses can be carried out, when they are likely to show that the evaluation is sensitive to underlying data, knowledge or assumptions, how to interpret the results of sensitivity analysis, and how the outcome can be reported. We also provide access to an application to conduct sensitivity analysis.

Automated interpretation of comparison scores for firearm toolmarks on cartridge case primers

An automated approach for evaluating the strength of the evidence of firearm toolmark comparison results is presented for a common source scenario. First, comparison scores are derived describing the similarity of marks typically encountered on the primer of fired cartridge cases: aperture shear striations as well as breechface and firing pin impressions. Subsequently, these scores are interpreted using reference distributions of comparison scores obtained for representative known matching (KM) and known non-matching (KNM) ballistic samples in a common source, score-based likelihood ratio (LR) system. We study various alternatives to set up such an LR system and compare them using qualitative and quantitative criteria known from the literature. As an example, results are applied to establish a system suitable for a firearm-ammunition combination often encountered in casework: Glock firearms with Fiocchi nickel primer ammunition. The system outputs an LR and a measure of LR uncertainty. The range of possible LR-values is limited to a minimum and maximum value in areas of the score domain with little reference data. Finally, the feasibility of combining LRs of different mark types into one LR for the entire primer is assessed. For the distribution models considered in this paper, different modeling approaches are optimal for different types of similarity scores. For the chosen firearm-ammunition combination, non-parametric Kernel Density Estimation (KDE) models perform best for similarity scores based on the correlation coefficient, whereas parametric models perform best for the Congruent Matching Cells (CMC) scores, assuming binomial and beta-binomial models for KM and KNM score distributions respectively. Finally, it is demonstrated that individual LRs of different mark types can be combined into one LR, to interpret a set of different marks on the primer as a whole.

A Review of Probabilistic Genotyping Systems: EuroForMix, DNAStatistX and STRmix™

Probabilistic genotyping has become widespread. EuroForMix and DNAStatistX are both based upon maximum likelihood estimation using a γ model, whereas STRmix™ is a Bayesian approach that specifies prior distributions on the unknown model parameters. A general overview is provided of the historical development of probabilistic genotyping. Some general principles of interpretation are described, including: the application to investigative vs. evaluative reporting; detection of contamination events; inter and intra laboratory studies; numbers of contributors; proposition setting and validation of software and its performance. This is followed by details of the evolution, utility, practice and adoption of the software discussed.

How can courts take into account the uncertainty in a likelihood ratio?

As legal practitioners and courts become more aware of scientific methods and evidence evaluation, they are demanding measures of the reliability of expert opinion. In particular, there are calls for error rates to accompany opinion evidence in comparative forensic sciences. While error rates or confidence intervals can be useful for those disciplines that claim to identify the source of a trace, the call for these statistical tools has extended to sciences that present opinions in the form of a likelihood ratio. In this article we argue against presenting both a likelihood ratio and numerical measures of its uncertainty. We explain how the LR already encapsulates uncertainty. Instead we consider how sensitivity analyses can be used to guide the presentation of LRs that are informative to the court and not unfair to defendants.

The Limits of Bayesian Thinking in Court

We comment on the contributions of Dahlman and of Fenton et al., who both suggested a Bayesian approach to analyze the Simonshaven case. We argue that analyzing a full case with a Bayesian approach is not feasible, and that there are serious problems with assigning actual numbers to probabilities and priors. We also discuss the nature of Bayesian thinking in court, and the nature and interpretation of the likelihood ratio. In particular, we discuss what it could mean that a likelihood ratio is in some sense uncertain.

A method for calculating the strength of evidence associated with an earwitness's claimed recognition of a familiar speaker

The present paper proposes and demonstrates a method for assessing strength of evidence when an earwitness claims to recognize the voice of a speaker who is familiar to them. The method calculates a Bayes factor that answers the question: What is the probability that the earwitness would claim to recognize the offender as the suspect if the offender was the suspect versus what is the probability that the earwitness would claim to recognize the offender as the suspect if the offender was not the suspect but some other speaker from the relevant population? By "claim" we mean a claim made by a cooperative earwitness not a claim made by an earwitness who is intentionally deceptive. Relevant data are derived from naïve listeners' responses to recordings of familiar speakers presented in a speaker lineup. The method is demonstrated under recording conditions that broadly reflect those of a real case.

Forensic likelihood ratio: Statistical problems and pitfalls

This article is a response to the position papers published in the Science & Justice virtual special issue on measuring and reporting the precision of forensic likelihood ratios. I point out a number of serious statistical errors in some of these papers. These issues need to be properly addressed before the philosophical debate can be conducted in earnest.