The Bayes factor in environmental forensic inference - with an application to ashes in dispute.
Anders Nordgaard (Swedish National Laboratory of Forensic Science)
Tuesday 28th October, 2014 15:00-16:00 Maths 515
For a private person (or a company without special authorisation) there are often strict regulations about what kind of material is allowed to be burnt in the open air or incinerated. This is because of the potential content of substances injurious to the health or the environment, such as toxins and heavy metals, in materials of unknown status. When there are suspicions that non-permitted material has been burnt the ashes from the fire are sent for analysis to a laboratory. The output from such an analysis may then indicate the presence of a number of injurious substances at different concentrations. The question is whether this result supports a hypothesis that non-permitted material was burnt or not.
Considering this problem as a forensic one, the ultimate goal is to obtain the posterior probability that non-permitted material was burnt given the data from the analysis of the ashes. To separate the roles of this procedure the laboratory should deliver the Bayes factor for the inference to be made, and leave prior probabilities to be assigned by the investigator. Since there are several substances monitored in the analysis and the measurements are on a continuous scale, the development of a Bayes factor is not straightforward. Here we show how a parametric approach can be used to model the probability distributions of different heavy metals under different hypotheses about the material burnt. We further discuss to what extent the substances may contribute individually to the Bayes factor, hence avoiding the use of a multivariate model.