Dismissal of the illusion of uncertainty in the assessment of a likelihood ratio

Abstract

The use of the Bayes factor or likelihood ratio as a metric to assess the probative value of forensic traces is largely supported by operational standards and recommendations in di↵erent forensic disciplines. However, the progress towards more widespread consensus about foundational principles is still fragile as it raises new problems about which views di↵er. It is not uncommon, for example, to encounter scientists who feel the need to compute the probability distribution of a given expression of evidential value (i.e., a Bayes factor), or to place intervals or significance probabilities on such a quantity. The paper here presents arguments to show that such views involve a misconception of principles and abuse of language. The conclusion of the discussion is that, in a given case at hand, forensic scientists ought to o↵er to a Court of justice a given single value for the Bayes factor, rather than an expression based on a distribution over a range of values.

Bayesian approach to LR assessment in case of rare type match

“…With the exception of little literature (e.g. DAWID and MORTERA (); BRüMMER and SWART (); TARONI et al ()), this point is generally mistaken and the problem is split into two phases. A Bayesian estimate of θ using B , in the form of a posterior expectation, is obtained and then plugged into a frequentist‐defined .…”

Avoiding overstating the strength of forensic evidence: Shrunk likelihood ratios/Bayes factors

“…An option for uninformative priors is to use Jeffreys reference priors, for which the values for the hyperparameters κ prior , β prior , and α prior are 0, 0, and −½ respectively (the value of μ prior is irrelevant since it is always multiplied by κ prior = 0). 10 Substituting these hyperparameter values into Eq. (3) and simplifying leads to Eq.…”

“…(5), as shown in Eq. (6), in whichσ 2 is the pooled sample variance 10 Note that the Jeffreys reference priors are improper priors with distributions that do not integrate to 1 and that cannot be graphically represented. The pseudodata interpretation also breaks down.…”

“…For discussion and examples of approaches of this sort, see [1][2][3][4][5][6][7][8][9]. From a subjectivist Bayesian perspective, there are no true but unknown population distributions, and the value of a Bayes factor (which is the Bayesian counterpart of the frequentist likelihood ratio) is a state of belief, not an estimate of a true but unknown value (in the context of evaluation of forensic evidence, this position is espoused in, for example [10,11]). Calculation of a Bayesian posterior predictive distribution is based not only on sample statistics but also on prior distributions for parameter values.…”

On the reproducibility and repeatability of likelihood ratio in forensics: A case study using face biometrics

“…Taroni et al [31] in their study argue on the way evidential value is presented in a court of law. The authors believe that it should be presented in a form of single value derived from Bayesian Factor (BF) rather than an expression based on a distribution over a range of values.…”