Robert G. Cowell

Mixture reduction via predictive scores

This paper explores the problem of reducing a mixture of conjugate priors to a smaller mixture, from the perspective of the application of a distance measure between priors. The analysis focuses on mixtures of Dirichlet priors, but it has wider applicability. In respect to the proposed scheme, it emerges that for mixtures of β-distributions a simple moment-matching reduction procedure is optimal and very good for the more general case of Dirichlet mixtures.

Probabilistic expert systems for handling artifacts in complex DNA mixtures

This paper presents a coherent probabilistic framework for taking account of allelic dropout, stutter bands and silent alleles when interpreting STR DNA profiles from a mixture sample using peak size information arising from a PCR analysis. This information can be exploited for evaluating the evidential strength for a hypothesis that DNA from a particular person is present in the mixture. It extends an earlier Bayesian network approach that ignored such artifacts. We illustrate the use of the extended network on a published casework example.

A gamma model for {DNA} mixture analyses

We present a new methodology for analysing forensic identification problems involving DNA mixture traces where several individuals may have contributed to the trace. The model used for identification and separation of DNA mixtures is based on a gamma distribution for peak area values. In this paper we illustrate the gamma model and apply it on several real examples from forensic casework.

FINEX: a Probabilistic Expert System for forensic identification.

A series of recent papers have shown how to formulate complex problems of forensic DNA identification inference, such as occur in disputed paternity or criminal identification cases, in terms of Probabilistic Expert Systems (PESs). However, at the present time, general purpose PES software is not particularly well suited to the repetitive tasks of: specifying an appropriate set of marker networks for a specific problem; for editing the many local conditional probability tables; and combining evidence from several genetic markers to evaluate likelihoods. Here, I describe a user-friendly prototype software tool called FINEX developed both to automate such tasks and also to evaluate likelihoods of interest. Ease of use is achieved by a graphical specification language that enables a user to quickly specify a range of forensic DNA problems. I describe the algorithms by which FINEX converts the user input in the graphical specification language and data on observed markers to the Bayesian networks used in PES.

Efficient maximum likelihood pedigree reconstruction

A simple and efficient algorithm is presented for finding a maximum likelihood pedigree using microsatellite (STR) genotype information on a complete sample of related individuals. The computational complexity of the algorithm is at worst (O(n(3)2(n))), where n is the number of individuals. Thus it is possible to exhaustively search the space of all pedigrees of up to thirty individuals for one that maximizes the likelihood. A priori age and sex information can be used if available, but is not essential. The algorithm is applied in a simulation study, and to some real data on humans.

Validation of an STR peak area model

In analyzing a DNA mixture sample, the measured peak areas of alleles of STR markers amplified using the polymerase chain-reaction (PCR) technique provide valuable information concerning the relative amounts of DNA originating from each contributor to the mixture. This information can be exploited for the purpose of trying to predict the genetic profiles of those contributors whose genetic profiles are not known. The task is non-trivial, in part due to the need to take into account the stochastic nature of peak area values. Various methods have been proposed suggesting ways in which this may be done. One recent suggestion is a probabilistic expert system model that uses gamma distributions to model the size and stochastic variation in peak area values. In this paper we carry out a statistical analysis of the gamma distribution assumption, testing the assumption against synthetic peak area values computer generated using an independent model that simulates the PCR amplification process. Our analysis shows the gamma assumption works very well when allelic dropout is not present, but performs less and less well as dropout becomes more and more of an issue, such as occurs, for example, in Low Copy Template amplifications.

A simple greedy algorithm for reconstructing pedigrees.

This paper introduces a simple greedy algorithm for searching for high likelihood pedigrees using micro-satellite (STR) genotype information on a complete sample of related individuals. The core idea behind the algorithm is not new, but it is believed that putting it into a greedy search setting, and specifically the application to pedigree learning, is novel. The algorithm does not require age or sex information, but this information can be incorporated if desired. The algorithm is applied to human and non-human genetic data and in a simulation study.

Causal discovery through MAP selection of stratified chain event graphs

We introduce a subclass of chain event graphs that we call stratified chain event graphs, and present a dynamic programming algorithm for the optimal selection of such chain event graphs that maximizes a decomposable score derived from a complete independent sample. We apply the algorithm to such a dataset, with a view to deducing the causal structure of the variables under the hypothesis that there are no unobserved confounders. We show that the algorithm is suitable for small problems. Similarities with and differences to a dynamic programming algorithm for MAP learning of Bayesian networks are highlighted, as are the relations to causal discovery using Bayesian networks.

CATFACT: Computer algebraic tools for applications of catastrophe theory

We describe the current state of a package, written in REDUCE, that is being developed to solve the following problems that arise in applications of elementary catastrophe theory. For an input unfolding of some singularity, the recognition problem is to find a set of topological invariants that fix the equivalence class of the singularity. If the modality invariant is less than 3 then normal forms for unfoldings are known. The recognition algorithm employs the Buchberger Algorithm for Grobner bases modified to the local requirements of singularity theory. The mapping problem is to find the taylor polynomial, up to any desired degree, of the right-equivalence that transforms the given unfolding into its normal form.

Combining allele frequency uncertainty and population substructure corrections in forensic DNA calculations

In forensic DNA calculations of relatedness of individuals and in DNA mixture analyses, at least two sources of uncertainty are present concerning the allele frequencies used for evaluating genotype probabilities when evaluating likelihoods. They are: (i) imprecision in the estimates of the allele frequencies in the population by using an inevitably finite database of DNA profiles to estimate them; and (ii) the existence of population substructure. Green and Mortera [6] showed that these effects may be taken into account individually using a common Dirichlet model within a Bayesian network formulation, but that when taken in combination this is not the case; however they suggested an approximation that could be used. Here we develop a slightly different approximation that is shown to be exact in the case of a single individual. We demonstrate the numerical closeness of the approximation using a published database of allele counts, and illustrate the effect of incorporating the approximation into calculations of a recently published statistical model of DNA mixtures.