Reconciliation of subjective probabilities and frequencies in forensic science

There is a continuous flow of articles published in legal and scientific journals that recite outworn direct or subtle attacks on Bayesian reasoning and/or the use of the subjective or personalistic interpretation of probability. An example is the recent paper written by Kaplan et al. [1] who, by referring to Kafadar’s review paper [2], opined, but did not justify, that there is a ‘[...] need to reduce subjectivity in the evaluation of forensic science’ and argued that ‘[...] the view presented here supports the use of objective probabilities.’ [1, at p. 108]. To understand why the objection on the use of subjective probability is not persuasive and why the widely claimed objective probabilities do not exist, one must first scrutinise the historically competing interpretations of probability
and their associated definitions. The basis of the defence of the use of the subjectivist interpretation of probability is the understanding of the simple points, misunderstood by critics, that subjectivity is not a synonym for arbitrariness and that the implementation of subjectivism does not neglect the use of the acquired knowledge that is often available in terms of relative frequencies. We will illustrate these points by reference to practical applications in forensic science where probabilities are often represented by relative frequencies. In this regard, our discussion clarifies the connection and the distinction between probabilities and frequencies. Specifically, we emphasise that
probability is an expression of our personal belief, an interpretation not to be equated with relative frequency as a mere summary of data. Our argument reveals the inappropriateness of attempts to interpret relative frequencies as probabilities, and naturally solves common problems that derive from such attempts. Further we emphasise that, despite the fact that they can be given an explicit role in probability assignments, neither are relative frequencies a necessary condition for such assignments nor, in forensic applications that consider events for which probabilities need to be specified, need they be meaningfully conceptualised in a frequentist perspective.