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Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science, 2nd Edition by Colin Aitken, Paolo Garbolino, Silvia Bozza, Alex Biedermann, Franco Taroni

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11.2.2 Probability assignment as a question of decision making

11.2.2.1 Scoring probability statements: Proper scoring rules

Generally, proper scoring rules enable a clear definition of probability in the context of an assignation of a probability to an event E. To apply such a proper scoring rule, a person—in the context here an expert or a scientist—is asked what probability he/she assigns to a given event E. This question is accompanied with the information that the probability statement thus elicited will be scored, with respect to the actual truth or falsity of E, denoted by, respectively, 1 and 0. This constraint is added as an incentive for persons to report their true beliefs, rather than a deliberately chosen value (i.e. one that is different from the one they have in mind).

This topic is of interest in forensic contexts as it often happens that scientists report categorical conclusions rather than genuine evaluations of probability. As an example, consider the notion of relevance that expresses the relationship between a given stain or trace and the offender. According to Stoney, the probability of relevance ‘(...) may range from very likely to practically nil (...)’ (Stoney 1994, p. 18). Such a probability assignment relates to the proposition of the kind ‘the stain or mark comes from (or was left by) the offender’ and appears as a factor in various likelihood ratio developments, such as for the evaluation of footwear marks (Evett et al. 1998b). Typically, one should ...

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