Data analysis in forensic science : a Bayesian decision by Franco Taroni; Wiley InterScience (Online service); et al

By Franco Taroni; Wiley InterScience (Online service); et al

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Further concepts and discussion are thus needed for examining whether scientists’ analyses, evaluations and reportings are trustworthy. Among these is an approach to the description of uncertainty as well as rules that prescribe the combination of expressions of uncertainty. For this purpose, Chapter 2 will outline in detail a method for calculating with beliefs that is part of a package that also contains a procedure to use personal beliefs to inform decision making. As will be seen, these elements represent the fundamental tenets of the discipline of statistics (Lindley 2000b).

If the answer is yes, then the theory cannot be applied. This is not an issue that is of direct interest for forensic scientists, because their decisions consider the analysis of data and not the final decision of a trial. Something will be said about this issue at the end of the chapter. Last but not least, consider the second axiom in both of the two versions that have been presented: preferences are invariant with respect to compound gambles and Savage’s ‘sure-thing principle’. This axiom is a rationality condition: it requires that in your system of preferences compound gambles like (f , h; α, 1 − α) and (g, h; α, 1 − α) be ranked as simple ones like f and g.

The probabilities of the events E can also depend upon your decision, so that your probability pij of ej given decision di can be different from your probability pkj of the same event given another decision dk . You are supposed to follow a rational policy for assigning degrees of belief to states of nature, so that each feasible decision is a ‘gamble’ di = (ci 1 , . . , cin ; pi 1 , . . , pin ) consisting of the consequences ci 1 , . . , cin , with probabilities pi 1 , . . , pin , such that nj=1 pij = 1.

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