Statistics and the Evaluation of Evidence for Forensic Scientists. Franco Taroni
They think a little more and remembers that, not only do the genotypes correspond, but also that they are both of type
(see Section 3.5). He is still not too sure what this means but feels that it is more representative of the information available to him than the previous probability, since it takes account of the actual genotypes of the crime stain and the PoI.
The genotype of the crime stain for locus LDLR is
1 (1) The probability that two people chosen at random have the same genotype for locus LDLR. This is 0.379.
2 (2) The probability that two people chosen at random have the same, pre‐specified, genotype. For genotype this is 0.103.
3 (3) The probability that one person, chosen at random, has the same genotype as the crime stain. If the crime stain is of group , this probability is 0.321, from Table 1.1.
The relative merits of these answers will be discussed in Section 3.5 for (1) and (2) and Section 2.4.5 for (3).
The phrase at random is taken to include the caveat that the people chosen are unrelated to the PoI. In practice, the phrase at random is not considered in its scientific usage (a person chosen accordingly to a randomising device). Note that, as expressed by Balding and Steele (2015),
It is important to keep in mind that in any crime investigation, random man is pure fiction: nobody was actually chosen at random in any population, and so probabilities calculated under an assumption of randomly sampled suspects have no direct bearing on evidential weight in actual cases. (p. 160)
A comment on randomness is also made by Kingston and Kirk (1964) (see pp. 515–516). A discussion about the extension of the concept of ‘random man’ to the one of ‘unrelated person’ to the PoI, when dealing with DNA evidence evaluation, is discussed in Milot et al. (2020).
1.3.3 Glass Fragments
Section 1.3.2 discussed an example of the interpretation of the evidence of DNA profiling. Consider now an example concerning glass fragments and the measurement of the refractive index of these.
Example 1.2 As before, consider the investigation of a crime. A window has been broken during the commission of the crime. A PoI is found with fragments of glass on their clothing, similar in refractive index to the broken window. Several fragments are taken for investigation and their refractive index measurements taken.
Note that there is a difference here from Example 1.1, where it was assumed that the crime stain had come from the criminal and been transferred to the crime scene. In Example 1.2 glass is transferred from the crime scene to the criminal. Glass on the PoI need not have come from the scene of the crime; it may have come from elsewhere and by perfectly innocent means. This is an asymmetry associated with this kind of scenario. The evidence is known as transfer evidence, as discussed in Section 1.1, because evidence (e.g. blood or glass fragments) has been transferred from the criminal to the scene or vice versa. Transfer from the criminal to the scene has to be considered differently from evidence transferred from the scene to the criminal. A full discussion of this is given in Chapters 5 and 6 .
Comparison in Example 1.2 has to be made between the two sets of fragments on the basis of their refractive index measurements. The evidential value of the outcome of this comparison has to be assessed. Notice that it is assumed that none of the fragments has any distinctive features and comparison is based only on the refractive index measurements.
Methods for evaluating such evidence were discussed in many papers in the late 1970s and early 1980s Evett (1977, 1978), Evett and Lambert (1982, 1984, 1985), Grove (1981, 1984), Lindley (1977c), Seheult (1978), and Shafer (1982). These methods will be described as appropriate in Chapters 3 and 7. Knowledge‐based computer systems have been developed. See Curran and Hicks (2009) and Curran (2009) for a review of practices in the forensic evaluation of glass and DNA evidence. As an aside, sophisticated systems have been developed to deal with DNA, notably DNA mixtures complexities (i.e. number of donors, peaks heights). Examples are presented and evaluated in Bright et al. (2016), Alladio et al. (2018), and Bleka et al. (2019).
Evett (1977) gave an example of the sort of problem that may be considered and developed a procedure for evaluating the evidence that mimicked the interpretative thinking of the forensic scientist of the time. The case is an imaginary one. Five fragments from a suspect are to be compared with 10 fragments from a window broken at the scene of a crime. The values of the refractive index measurements are given in Table 1.2. The procedure developed by Evett is a two‐stage one. It is described here briefly. It is a rather arbitrary and hybrid procedure. While it follows the thinking of the forensic scientist, there are interpretative problems, which are described here, in attempting to provide due value to the evidence. An alternative approach that overcomes these problems is described in Chapter 7 .
Table 1.2 Refractive index measurements.
Measurements from the window | 1.518 44 | 1.518 48 | 1.518 44 | 1.518 50 | 1.518 40 |
1.518 48 | 1.518 46 | 1.518 46 | 1.518 44 | 1.518 48 | |
Measurements from the PoI | 1.518 48 | 1.518 50 | 1.518 48 | 1.518 44 | 1.518 46 |
The first stage is known as the comparison stage. The two sets of measurements are compared. The comparison takes the form of the calculation of a statistic,