The subjectivist interpretation of probability and the problem of individualisation in forensic science

This paper presents and discusses further aspects of the subjectivist interpretation of probability (also known as the ‘personalist’ view of probabilities) as initiated in earlier forensic and legal literature. It shows that operational devices to elicit subjective probabilities – in particular the so-called scoring rules – provide additional arguments in support of the standpoint according to which categorical claims of forensic individualisation do not follow from a formal analysis under that view of probability theory.     

Equal prior probabilities: can one do any better?

This paper discusses recommendations concerning the use of prior probabilities that underlie recent, but in no way novel, proposals of presenting scientific evidence in terms of posterior probabilities, in the context sometimes referred to as the 'full Bayes' approach'. A chief issue of this procedure is a proposal that--given the unavailability of case-specific circumstantial information--scientists should consider the prior probabilities of the propositions under which scientific evidence is evaluated as equal. The discussion presented here draws the reader's attention to the fact that the philosophical foundations of such a recommendation (in particular, attempted justifications through the Principle of Maximum Entropy (PME)) are far more controversial than what is actually admitted by the advocates for their use in the theory and practice of forensic science. Invoking only basic assumptions and the mathematical rules of probability calculus, the authors of this paper propose an argument that shows that there can be other more feasible and defensible strategies for eliciting reasonable prior probabilities. It is solely demanded that the reasoner is willing to make up his mind seriously on certain standard issues of fairly general criminal cases, such as evidential relevance or the probability of a suspect's guilt. However, because these issues intimately pertain to the responsibility of the trier of the fact, it is argued here that scientists' attempts to define appropriate prior probabilities should continue to be considered as untenable for the need.     

Two items of evidence, no putative source: an inference problem in forensic intelligence

Intelligence analysts commonly associate cases on the basis of similarities found in compared characteristics of scientific evidence. The present paper studies some of the inferential difficulties associated with such operations. An analysis is proposed that breaks down the reasoning process into inference to common source, and inference to case linkage. The former requires an approach to the difficulty associated with evaluating the similarities of items of evidence from different cases with no putative source being available. The latter requires consideration to be given to the relevance of evidence. Throughout the paper, probability theory is used to describe the nature of the proposed inferences. Graphical models are also introduced with the aim of providing further insight into the dependence and independence relationships assumed to hold among the various propositions considered. Notions from decision theory are used to discuss ways in which intelligence analysts may assist investigators in deciding whether or not cases should be considered as linked.     

The evaluation of evidence in the forensic investigation of fire incidents. Part II. Practical examples of the use of Bayesian networks

This paper extends a previous discussion of the use of Bayesian networks for evaluating evidence in the forensic investigation of fire incidents. Bayesian networks are proposed for two casework examples and the practical implications studied in detail. Such networks were found to provide precious support in addressing some of the wide range of issues that affect the coherent evaluation of evidence.     

The database search problem: A question of rational decision making

This paper applies probability and decision theory in the graphical interface of an influence diagram to study the formal requirements of rationality which justify the individualization of a person found through a database search. The decision-theoretic part of the analysis studies the parameters that a rational decision maker would use to individualize the selected person. The modeling part (in the form of an influence diagram) clarifies the relationships between this decision and the ingredients that make up the database search problem, i.e., the results of the database search and the different pairs of propositions describing whether an individual is at the source of the crime stain. These analyses evaluate the desirability associated with the decision of 'individualizing' (and 'not individualizing'). They point out that this decision is a function of (i) the probability that the individual in question is, in fact, at the source of the crime stain (i.e., the state of nature), and (ii) the decision maker's preferences among the possible consequences of the decision (i.e., the decision maker's loss function). We discuss the relevance and argumentative implications of these insights with respect to recent comments in specialized literature, which suggest points of view that are opposed to the results of our study.     

Uncertainty about the true source. A note on the likelihood ratio at the activity level

This paper focuses on likelihood ratio based evaluations of fibre evidence in cases in which there is uncertainty about whether or not the reference item available for analysis - that is, an item typically taken from the suspect or seized at his home - is the item actually worn at the time of the offence. A likelihood ratio approach is proposed that, for situations in which certain categorical assumptions can be made about additionally introduced parameters, converges to formula described in existing literature. The properties of the proposed likelihood ratio approach are analysed through sensitivity analyses and discussed with respect to possible argumentative implications that arise in practice.     

Bayesian networks and the value of the evidence for the forensic two-trace transfer problem*

Forensic scientists face increasingly complex inference problems for evaluating likelihood ratios (LRs) for an appropriate pair of propositions. Up to now, scientists and statisticians have derived LR formulae using an algebraic approach. However, this approach reaches its limits when addressing cases with an increasing number of variables and dependence relationships between these variables. In this study, we suggest using a graphical approach, based on the construction of Bayesian networks (BNs). We first construct a BN that captures the problem, and then deduce the expression for calculating the LR from this model to compare it with existing LR formulae. We illustrate this idea by applying it to the evaluation of an activity level LR in the context of the two-trace transfer problem. Our approach allows us to relax assumptions made in previous LR developments, produce a new LR formula for the two-trace transfer problem and generalize this scenario to n traces.     

Analysing and exemplifying forensic conclusion criteria in terms of Bayesian decision theory

There is ongoing discussion in forensic science and the law about the nature of the conclusions reached based on scientific evidence, and on how such conclusions – and conclusion criteria – may be justified by rational argument. Examples, among others, are encountered in fields such as fingermarks (e.g., ‘this fingermark comes from Mr. A's left thumb’), handwriting examinations (e.g., ‘the questioned signature is that of Mr. A’), kinship analyses (e.g., ‘Mr. A is the father of child C’) or anthropology (e.g., ‘these are human remains'). Considerable developments using formal methods of reasoning based on, for example (Bayesian) decision theory, are available in literature, but currently such reference principles are not explicitly used in operational forensic reporting and ensuing decision-making. Moreover, applied examples, illustrating the principles, are scarce. A potential consequence of this in practical proceedings, and hence a cause of concern, is that underlying ingredients of decision criteria (such as losses quantifying the undesirability of adverse decision consequences), are not properly dealt with. There is merit, thus, in pursuing the study and discussion of practical examples, demonstrating that formal decision-theoretic principles are not merely conceptual considerations. Actually, these principles can be shown to underpin practical decision-making procedures and existing legal decision criteria, though often not explicitly apparent as such. In this paper, we will present such examples and discuss their properties from a Bayesian decision-theoretic perspective. We will argue that these are essential concepts for an informed discourse on decision-making across forensic disciplines and the development of a coherent view on this topic. We will also emphasize that these principles are of normative nature in the sense that they provide standards against which actual judgment and decision-making may be compared. Most importantly, these standards are justified independently of peoples' observable decision behaviour, and of whether or not one endorses these formal methods of reasoning.