What should a forensic practitioner's likelihood ratio be? II.

In the debate as to whether forensic practitioners should assess and report the precision of the strength of evidence statements that they report to the courts, I remain unconvinced by proponents of the position that only a subjectivist concept of probability is legitimate. I consider this position counterproductive for the goal of having forensic practitioners implement, and courts not only accept but demand, logically correct and scientifically valid evaluation of forensic evidence. In considering what would be the best approach for evaluating strength of evidence, I suggest that the desiderata be (1) to maximise empirically demonstrable performance; (2) to maximise objectivity in the sense of maximising transparency and replicability, and minimising the potential for cognitive bias; and (3) to constrain and make overt the forensic practitioner's subjective-judgement based decisions so that the appropriateness of those decisions can be debated before the judge in an admissibility hearing and/or before the trier of fact at trial. All approaches require the forensic practitioner to use subjective judgement, but constraining subjective judgement to decisions relating to selection of hypotheses, properties to measure, training and test data to use, and statistical modelling procedures to use - decisions which are remote from the output stage of the analysis - will substantially reduce the potential for cognitive bias. Adopting procedures based on relevant data, quantitative measurements, and statistical models, and directly reporting the output of the statistical models will also maximise transparency and replicability. A procedure which calculates a Bayes factor on the basis of relevant sample data and reference priors is no less objective than a frequentist calculation of a likelihood ratio on the same data. In general, a Bayes factor calculated using uninformative or reference priors will be closer to a value of 1 than a frequentist best estimate likelihood ratio. The bound closest to 1 based on a frequentist best estimate likelihood ratio and an assessment of its precision will also, by definition, be closer to a value of 1 than the frequentist best estimate likelihood ratio. From a practical perspective, both procedures shrink the strength of evidence value towards the neutral value of 1. A single-value Bayes factor or likelihood ratio may be easier for the courts to handle than a distribution. I therefore propose as a potential practical solution, the use of procedures which account for imprecision by shrinking the calculated Bayes factor or likelihood ratio towards 1, the choice of the particular procedure being based on empirical demonstration of performance.