The two interrelated topics of this course are Graphical Models, and Forensic Statistics.
Forensic Statistics is the branch of applied statistics concerned with the preparation and communication of statistical evidence in criminal investigation and judicial proceedings. This generates statistical problems of a unique nature. In particular, in court proceedings the usual language of confidence regions, statistical tests, and so on, is not understood and arguably inappropriate. More generally, statistical problems concerning identification of persons or weapons from (poor quality) finger prints, DNA traces, spent bullets are appear similar to classical problems of discriminant analysis, but the data has a different structure, the question posed is a different question, and the answer has to be given in an unusual form. The statistician is called on to give a scientific opinion concerning the interpretation of concrete pieces of evidence. Since the statistician is involved precisely because the evidence is not clear-cut, his or her job is to inform the court of the degree to which the evidence supports one or the other parties in the dispute.
Graphical Models are one particular tool which have become extremely popular in recent years in forensic statistics. A graphical model is a mathematical representation of dependence and independence relationships between a number of variables. The joint probability distribution of those variables can be factored into components belonging to different parts of the graph. Computation of conditional distributions and of marginal distributions can be carried out by algorithms working on the graph. Graphical models become extremely powerful when we adopt a Bayesian point of view by which uncertainties of all kinds are modelled with probability distributions. In Bayesian statistics, the job of a statistician is simply to compute the probability distribution of key unknown variables, given the values of observed variables (the data). In forensic statistics, a prior distribution of guilt or innocence is innapropriate, but with a prior of 50/50, the posterior becomes simply the likelihood ratio.
In the course we’ll study how graphical models can be applied to forensic problems involving family relationships and DNA evidence, and look at the problems of applying them more widely.
First courses in probability and in statistics; preferably also a second (more advanced) course in statistics or in probability.
Forensic statistics: there does not yet exist a suitable book. I will make internet links to suitable literature, later. Graphical Models: S.L. Lauritzen (1996), Graphical Models, Clarendon Press, Oxford, United Kingdom.