A top-down approach to DNA mixtures

Presently, there exist many different models and algorithms for determining, in the form of a likelihood ratio, whether there is evidence that a person of interest contributed to a mixed trace profile. These methods have in common that they model the whole trace, hence all its contributors, which leads to the computation time being mostly determined by the number of contributors that is assumed. At some point, these calculations are no longer feasible. We present another approach, in which we target the contributors of the mixture in the order of their contribution. With this approach the calculation time now depends on how many contributors are queried. This means that any trace can be subjected to calculations of likelihood ratios in favor of being a relatively prominent contributor, and we can choose not to query it for all its contributors, e.g., if that is computationally not feasible, or not relevant for the case. We do so without using a quantitative peak height model, i.e., we do not define a peak height distribution. Instead, we work with subprofiles derived from the full trace profile, carrying out likelihood ratio calculations on these with a discrete method. This lack of modeling makes our method widely applicable. The results with our top-down method are slightly conservative with respect to the one of a continuous model, and more so as we query less and less prominent contributors. We present results on mixtures with known contributors and on research data, analyzing traces with plausibly 6 or more contributors. If a top-k of most prominent contributors is targeted, it is not necessary to know how many other contributors there are for LR calculations, and the more prominent the queried contributor is relatively to all others, the less the evidential value depends on the specifics of a chosen peak height model. For these contributors the qualitative statement that more input DNA leads to larger peaks suffices. The evidential value for a comparison with minor contributors on the other hand, potentially depends much more on the chosen model. We also conclude that a trace's complexity, as meaning its (in)ability to yield large LR's that are not too model-dependent, is not measured by its number of contributors; rather, it is the equality of contribution that makes it harder to obtain strong evidence

The analogy between DNA kinship and DNA mixture evaluation, with applications for the interpretation of likelihood ratios produced by possibly imperfect models

Two main applications of forensic DNA analysis are the investigation of possible relatedness and the investigation whether a person left DNA in a trace. Both of these are usually carried out by the calculation of likelihood ratios. In the kinship case, it is standard to let the likelihood ratio express the support in favour of the investigated relatedness versus no relatedness, and in the investigation of traces, one by default compares the hypothesis that the person of interest contributed DNA, versus that he is unrelated to any of the actual contributors. In both cases however, we can also view the probabilistic procedure as an inference of the profile of the person we look for: in other words, in both cases we carry out probabilistic genotyping. In this article we use this general analogy to develop various more specific analogies between kinship and mixture likelihood ratios. These analogies help to understand the concepts that play a role, and also to understand the importance of the statistical modeling needed for DNA mixtures. In this article, we apply our findings to consider what we can and cannot conclude from a likelihood ratio in favour of contribution to a mixed DNA profile, if that is computed by a model whose specifics are not entirely known to us, or where we do not know whether they provide a good description of the stochastic effects involved in the generation of DNA trace profiles. We show that, if unrelated individuals are adequately modeled, we can give bounds on how often LR's coming from certain types of black box models may arise, both for persons who are actual contributors and who are unrelated. In particular we show that no model, provided it satisfies basic requirements, can overestimate the evidence found for actual contributors both often and strongly

Response paper to “The likelihood of encapsulating all uncertainty”:The relevance of additional information for the LR

In this response paper, part of the Virtual Special Issue on “Measuring and Reporting the Precision of Forensic Likelihood Ratios”, we further develop our position on likelihood ratios which we described previously in Berger et al. (2016) “The LR does not exist”. Our exposition is inspired by an example given in Martire et al. (2016) “On the likelihood of encapsulating all uncertainty”, where the consequences of obtaining additional information on the LR were discussed. In their example, two experts use the same data in a different way, and the LRs of these experts change differently when new data are taken into account. Using this example as a starting point we will demonstrate that the probability distribution for the frequency of the characteristic observed in trace and reference material can be used to predict how much an LR will change when new data become available. This distribution can thus be useful for such a sensitivity analysis, and address the question of whether to obtain additional data or not. But it does not change the answer to the original question of how to update one's prior odds based on the evidence, and it does not represent an uncertainty on the likelihood ratio based on the current data

Evaluation of glass evidence at activity level:A new distribution for the background population

For evidence evaluation of the physicochemical properties of glass at activity level a well-known formula introduced by Evett & Buckleton [1,2] is commonly used. Parameters in this formula are, amongst others, the probability in a background population to find on somebody's clothing the observed number of glass sources and the probability in a background population to find on somebody's clothing a group of fragments with the same size as the observed matching group. Recently, for efficiency reasons, the Netherlands Forensic Institute changed its methodology to measure not all the glass fragments but a subset of glass fragments found on clothing. Due to the measurement of subsets, it is difficult to get accurate estimates for these parameters in this formula. We offer a solution to this problem. The heart of the solution consists of relaxing the assumption of conditional independence of group sizes of background fragments, and modelling the probability of an allocation of background fragments into groups given a total number of background fragments by a two-parameter Chinese restaurant process (CRP) [3]. Under the assumption of random sampling of fragments to be measured from recovered fragments in the laboratory, parameter values for the Chinese restaurant process may be estimated from a relatively small dataset of glass in other relevant cases. We demonstrate this for a dataset of glass fragments collected from upper garments in casework, show model fit and provide a prototypical calculation of an LR at activity level accompanied with a parameter sensitivity analysis for reasonable ranges of the CRP parameter values. Considering that other laboratories may want to measure subsets as well, we believe this is an important alternative approach to the evaluation of numerical LRs for glass analyses at activity level

Optimal strategies for familial searching

Familial searching is the process of finding potential relatives of the donor of a crime scene profile in a DNA database. Several authors have proposed strategies for generating candidate lists of potential relatives. This paper reviews four strategies and investigates theoretical properties as well as empirical behavior, using a comprehensive simulation study on mock databases. The effectiveness of a familial search is shown to highly depend on the case profile as well as on the tuning parameters. We give recommendations for proceeding in an optimal way and on how to choose tuning parameters both in general and on a case-by-case basis. Additionally we treat searching heterogeneous databases (not all profiles comprise the same loci) and composite searching for multiple types of kinship. An R-package for reproducing results in a particular case is released to help decision-making in familial searching. © 2014 Elsevier Ireland Ltd