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To test or not to test? A question of rational decision making in forensic biology

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Abstract

How can the forensic scientist rationally justify performing a sequence of tests and analyses in a particular case? When is it worth performing a test or analysis on an item? Currently, there is a large void in logical frameworks for making rational decisions in forensic science. The aim of this paper is to fill this void by presenting a step-by-step guide on how to apply Bayesian decision theory to routine decision problems encountered by forensic scientists on performing or not performing a particular laboratory test or analysis. A decision-theoretic framework, composed of actions, states of nature, and utilities, models this problem, and an influence diagram translates its notions into a probabilistic graphical network. Within this framework, the expected value of information (EVOI) for the submission of an item to a particular test or analysis addresses the above questions. The development of a classical case example on whether to perform presumptive tests for blood before submitting the item for a DNA analysis illustrates the use of this model for source level questions in forensic biology (i.e., questions that ask whether a crime stain consisting of a particular body fluid comes from a particular person). We show how to construct an influence diagram for this example, and how sensitivity analyses lead to an optimal analytical sequence. The key idea is to show that such a Bayesian decisional approach provides a coherent framework for justifying the optimal analytical sequence for a particular case in forensic science.

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Notes

  1. As opposed to whom the DNA comes from, because there could be background DNA unrelated to the assault on the surface of the bloodstain(s).

  2. We use the word "coherent" following Lindley (1985), p. 22:

    (...) it will not be possible to say that a decision is right but only that these decisions cohere, or not. It is the relationships between events or decisions that matter, not the individual events or decisions.

    Hence, a normative framework provides constraints that ensure coherence in decision making. These constraints demand that the decision maker’s degrees of belief in uncertain events, as well as his or her degrees of satisfaction with the choices’ possible consequences, obey the laws of probability.

  3. The list is exhaustive when the decision maker inevitably chooses one of the actions in the list. Note that if it is possible for the decision maker to do nothing, then this possibility must be defined as one of the actions for the action space to be exhaustive.

  4. The actions are mutually exclusive if the decision maker can never choose more than one of them at one time.

  5. A discussion on the role of subjective probabilities and their relation with frequencies is introduced in Taroni et al. (2018).

  6. A gamble between two outcomes means that one of them will occur with a probability p and the other with a probability \((1-p)\).

  7. A Bayesian network (BN) is a graphical probability model containing only random variables as nodes (e.rg., Jensen and Nielsen 2007; Kjaerulff and Madsen 2008).

  8. Note that the forensic scientist here is interested specifically in obtaining the DNA profile of a bloodstain, and is not interested in the DNA profile of any other biological material of human origin that may be present on the surface on which the stain was recovered.

  9. We purposely did not specify a monetary unit, as these costs will vary from lab to lab and from country to country, and these numbers are for illustrative purposes only.

  10. The literature also commonly uses the terms sensitivity and specificity, which are \(1-\beta\) and \(1-\alpha\), respectively.

  11. For example, was a gorilla present on the crime scene? Or, more realistically, what is the probability that the surface on which the trace was recovered was freshly cleaned with a bleach solution?

  12. These extremes represent perfect information which attain the maximum utility values for performing a DNA analysis (i.e., \(u(O_{11})\)) and for not performing a DNA analysis (i.e., \(u(O_{2-})\)).

  13. Here, the maximum expected utility without the test is equal to \(Pr(B|I) \times u(O_{11}) + Pr(\lnot B|I) \times u(O_{12})\) for the Kastle-Meyer test (Fig. 4) and to \(Pr(\Theta _1|I) \times u(O_{11}) + Pr(\Theta _2|I) \times u(O_{12})\) for the Hexagon OBTI test (Fig. 5).

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Funding

This research was funded by the Swiss National Science Foundation grant numbers 100014-135340 and 100011 204554/1.

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Authors and Affiliations

  1. School of Criminal Justice, University of Lausanne, le Batochime, Quartier UNIL-Sorge, 1015, Lausanne, VD, Switzerland

    Simone Gittelson & Franco Taroni

  2. Department of Forensic Sciences, George Washington University, 2100 Foxhall Road NW, Washington, DC, 20007, USA

    Simone Gittelson

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  1. Simone Gittelson
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  2. Franco Taroni
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Conceptualization: FT; Methodology: SG; Formal analysis and investigation: SG; Writing—original draft preparation: SG; Writing—review and editing: SG and FT; Funding acquisition: FT.

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Correspondence to Simone Gittelson.

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Gittelson, S., Taroni, F. To test or not to test? A question of rational decision making in forensic biology. Artif Intell Law (2024). https://doi.org/10.1007/s10506-023-09386-3

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