1.1 Hat Example of Biedermann, Taroni and Thompson
Here, P(NoC = n|D, Hd) is the a posteriori probability to have n contributors when the PoI is not contributing and given the data D. The expressions P(NoC = n|Hp) and P(NoC = n|Hd) refer to the prior probabilities to have n contributors either under Hp or Hd. For these prior probabilities the genetic information D is not taken into account and they are solely determined by other case circumstances. Although they might be different for Hp and Hd, this is only in some cases sensible [
Let us now return to the case of either two or three contributors. For simplicity we assume that other NoCs are not possible. Then the sum consists only of two terms
We are interested in the situation that under Hp only tree contributors are possible. That means that LR(2) = 0 and we obtain the central equation
which we will investigate further in order to get leads about how to deal with the ambiguity in the NoC.
where LRd = P(D|NoC = 3, Hd)/P(D|NoC = 2, Hd). We see that P(NoC = 3|D, Hd) depends on the two terms LRd and P(NoC = 3) and we will consider these separately in the following.
3.1 The likelihood ratio LRd
3.2 The prior probability P(NoC=3)
3.3 Returning to the Hat Example
Conflict of interest statement
- Using graphical probability analysis (Bayes Nets) to evaluate a conditional DNA inclusion.Law Probab. Risk. 2011; 10: 89-121
- Fairness in evaluating DNA mixtures.Forensic Sci. Int. Genet. 2017; 27: 186
- Another response to “About the number of contributors to a forensic sample”.Forensic Sci. Int. Genet. 2017; 28: e11
- A response to “About the number of contributors to a forensic sample”.Forensic Sci. Int. Genet. 2017; 26: e9-e13
- About the number of contributors to a forensic sample.Forensic Sci. Int. Genet. 2016; 25: e18-e19
- Contributors are a nuisance (parameter) for DNA mixture evidence evaluation.Forensic Sci. Int. Genet. 2018; 37: 116-125