Institute of Environmental Science and Research Limited, Private Bag 92021, Auckland, 1142, New Zealand; University of Auckland, Department of Statistics, Auckland, New Zealand.
Forensic Science SA, 21 Divett Place, Adelaide, SA, 5000, Australia; School of Biological Sciences, Flinders University, GPO Box 2100, Adelaide, SA, 5001, Australia.
Forensic Sci Int Genet. 2021 Jan;50:102406. doi: 10.1016/j.fsigen.2020.102406. Epub 2020 Oct 22.
We seek to develop a rational approach to forming propositions when little information is available from the outset, as this often happens in casework. If propositions used when evaluating evidence are not exhaustive (in the context of the case), then there is a theoretical risk that an LR greater than one may be associated with a proposition in the numerator that - if all meaningful propositions had been considered - would in fact have a lower posterior probability after consideration of the evidence. Ideally, all propositions should be considered. However, with multiple propositions, some terms will be larger than others and for simplification very small terms can be neglected without changing the order of magnitude of the value of the evidence (i.e. LR). Our analysis shows that mathematically a contributor's DNA can be assumed to be present under both prosecution and alternative propositions (H and H) if there is a reasonable prior probability of their DNA being present and their inclusion is supported by the profile. This is because the terms associated to these sub-propositions will dominate our LR. For example, in the absence of specific information, when considering two persons of interest (POI) as potential contributors to a mixed DNA profile we suggest the assumption of one when examining the presence of the other, after checking that both collectively explain the profile well. This represents more meaningful propositions and allows better discrimination. Slooten and Caliebe have shown that the overall LR is the weighted average of LRs with the same number of contributors (NoC) under both propositions. The weights involve both an assessment of the probability of the crime scene DNA profile and the probability of this NoC given the background information.
我们试图在初始信息很少的情况下制定合理的命题形成方法，因为这种情况在案例工作中经常发生。如果在评估证据时使用的命题不完整（在案件背景下），那么就存在理论风险，即一个大于 1 的似然比可能与分子中的一个命题相关联，如果考虑到所有有意义的命题，那么这个命题实际上在考虑证据后会有更低的后验概率。理想情况下，所有命题都应该被考虑。然而，对于多个命题，有些术语会比其他术语大，为了简化，可以忽略非常小的术语，而不会改变证据的数量级（即似然比）。我们的分析表明，如果存在合理的先验概率，并且特征支持他们的包含，那么从数学上讲，可以假设在起诉和替代命题（H 和 H）下贡献者的 DNA 都存在。这是因为与这些子命题相关的术语将主导我们的似然比。例如，在没有具体信息的情况下，当考虑两个感兴趣的人（POI）作为混合 DNA 特征的潜在贡献者时，我们建议在检查另一个人的存在时，假设其中一个人存在，然后检查两者是否都能很好地解释特征。这代表了更有意义的命题，并允许更好的区分。Slooten 和 Caliebe 已经表明，总体似然比是两个命题下具有相同贡献者数量（NoC）的似然比的加权平均值。权重涉及对犯罪现场 DNA 特征的概率以及给定背景信息的这种 NoC 的概率的评估。
