Uncertainty about the true source. A note on the likelihood ratio at the activity level Franco Taroni a, *, Alex Biedermann a , Silvia Bozza b , Jennifer Comte a , Paolo Garbolino c a University of Lausanne, School of Criminal Justice, Switzerland b University Ca’ Foscari of Venice, Department of Economics, Italy c University IUAV of Venice, Department of Arts and Design, Italy 1. Introduction A model for the evaluation of the evidence through a likelihood ratio when the material is transferred during the commission of a crime has been proposed by Evett [8], and has since then be re-used in other publications [3,6,9]. More generally, this has led to the consideration that transfer and presence by chance of trace material on a receptor are fundamental factors when assessing evidence under so-called activity level propositions [4]. In many such contexts, it is reasonable to assume that recovered material has an undoubtable link with a given individual (which may be the suspect). That is to say, if there has been a direct and primary transfer, 1 then DNA found on a crime scene provides a direct connection between the source of that DNA and the crime scene. The reason for this is that biological material is intimately related to each individual. This may not be the case, however, with certain categories of evidence other than DNA, such as shoemarks or fibres. In particular, shoes or garments may have been worn by different individuals. Thus, one also needs to establish an association between a given donor item (such as a garment or a pair of shoes) and a given suspect in order to link that person to the action under investigation. This paper investigates the effect that the latter issue may have on the development of a likelihood ratio under activity level propositions. The argument will be illustrated through the use of probabilistic graphical models (Bayesian networks). The paper is organized as follows: Section 2 starts presenting the likelihood ratio as developed originally in [8]. This develop- ment along with its assumptions are taken here as part of accepted theory on the topic. Its derivation thus is not repeated in full detail. Instead, its main components will be stated in order to clarify from where the paper here proposes a further development. Section 3 introduces probabilistic graphical models, notably Bayesian net- works, which will be used in Section 4 to deal with scenarios of interest that point out the additional source of uncertainty that will be included in the existing approach. Section 5 develops the likelihood ratio formula guided by the graphical model previously presented in Section 4. The proposed likelihood ratio model is analysed through sensitivity analysis and discussed in Sections 6 and 7. 2. Likelihood ratios in scenarios involving DNA evidence: evidence left by the offender Imagine the following scenario. A crime has been committed during which a young woman was attacked by an assailant. Examination of the victim’s fingernails revealed the presence of Forensic Science International 220 (2012) 173–179 A R T I C L E I N F O Article history: Received 31 May 2011 Received in revised form 1 December 2011 Accepted 27 February 2012 Available online 23 March 2012 Keywords: Evidence evaluation Likelihood ratio Bayesian networks Hierarchy of propositions A B S T R A C T 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. ß 2012 Elsevier Ireland Ltd. All rights reserved. * Corresponding author. E-mail address: Franco.Taroni@unil.ch (F. Taroni). 1 A primary transfer is referred here to as an event in which a given donor sheds material in the first place (e.g., an injured offender leaves blood stains on a broken window). Secondary transfer (not considered in this paper) occurs, for example, if trace material on a suspect’s clothing (e.g., traces of illegal drugs acquired as a primary transfer due to manipulating drugs in powder form) is transferred to another surface (e.g., a car seat) [13]. Contents lists available at SciVerse ScienceDirect Forensic Science International jou r nal h o mep age: w ww.els evier .co m/lo c ate/fo r sc iin t 0379-0738/$ – see front matter ß 2012 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.forsciint.2012.02.021