Julia Mortera

Sensitivity of inferences in forensic genetics to assumptions about founding genes

Many forensic genetics problems can be handled using structured systems of discrete variables, for which Bayesian networks offer an appealing practical modeling framework, and allow inferences to be computed by probability propagation methods. However, when standard assumptions are violated—for example, when allele frequencies are unknown, there is identity by descent or the population is heterogeneous—dependence is generated among founding genes, that makes exact calculation of conditional probabilities by propagation methods less straightforward. Here we illustrate different methodologies for assessing sensitivity to assumptions about founders in forensic genetics problems. These include constrained steepest descent, linear fractional programming and representing dependence by structure. We illustrate nthese methods on several forensic genetics examples involving criminal identification, simple and complex disputed paternity and DNA mixtures.

Paternity testing that involves a DNA mixture

Here we analyse a complex disputed paternity case, where the DNA of the putative father was extracted from his corpse that had been inhumed for over 20 years. This DNA was contaminated and appears to be a mixture of at least two individuals. Furthermore, the mothers DNA was not available. The DNA mixture was analysed so as to predict the most probable genotypes of each contributor. The major contributors profile was then used to compute the likelihood ratio for paternity. We also show how to take into account a dropout allele and the possibility of mutation in paternity testing.

Object-oriented Bayesian networks for a decision support system for antitrust enforcement

We study an economic decision problem where the actors are two firms and the Antitrust Authority whose main task is to monitor and prevent firms potential anti-competitive behaviour and its effect on the market. The Antitrust Authoritys decision process is modelled using a Bayesian network where both the relational structure and the parameters of the model are estimated from a data set provided by the Authority itself. A number of economic variables that influence this decision process are also included in the model. We analyse how monitoring by the Antitrust Authority affects firms strategies about cooperation. Firms strategies are modelled as a repeated prisoners dilemma using object-oriented Bayesian networks. We show how the integration of firms decision process and external market information can be modelled in this way. Various decision scenarios and strategies are illustrated.

Paternity testing and other inference about relationships from DNA mixtures

We present methods for inference about relationships between contributors to a DNA mixture and other individuals of known genotype: a basic example would be testing whether a contributor to a mixture is the father of a child of known genotype. The evidence for such a relationship is evaluated as the likelihood ratio for the specified relationship versus the alternative that there is no relationship. We analyse real casework examples from a criminal case and a disputed paternity case; in both examples part of the evidence was from a DNA mixture. DNA samples are of varying quality and therefore present challenging problems in interpretation. Our methods are based on a recent statistical model for DNA mixtures, in which a Bayesian network (BN) is used as a computational device; the present work builds on that approach, but makes more explicit use of the BN in the modelling. The R code for the analyses presented is freely available as supplementary material. We show how additional information of specific genotypes relevant to the relationship under analysis greatly strengthens the resulting inference. We find that taking full account of the uncertainty inherent in a DNA mixture can yield likelihood ratios very close to what one would obtain if we had a single source DNA profile. Furthermore, the methods can be readily extended to analyse different scenarios as our methods are not limited to the particular genotyping kits used in the examples, to the allele frequency databases used, to the numbers of contributors assumed, to the number of traces analysed simultaneously, nor to the specific hypotheses tested.

Discussion of: "Statistical analysis of an archeological find"

Discussion of ``Statistical analysis of an archeological find by Andrey Feuerverger [arXiv:0804.0079]