Bayesian predictive modeling and comparison of oil samples

Statistical comparison of oil samples is an integral part of oil spill identification, which deals with the process of linking an oil spill with its source of origin. In current practice, a frequentist hypothesis test is often used to evaluate evidence in support of a match between a spill and a source sample. As frequentist tests are only able to evaluate evidence against a hypothesis but not in support of it, we argue that this leads to unsound statistical reasoning. Moreover, currently only verbal conclusions on a very coarse scale can be made about the match between two samples, whereas a finer quantitative assessment would often be preferred. To address these issues, we propose a Bayesian predictive approach for evaluating the similarity between the chemical compositions of two oil samples. We derive the underlying statistical model from some basic assumptions on modeling assays in analytical chemistry, and to further facilitate and improve numerical evaluations, we develop analytical expressions for the key elements of Bayesian inference for this model. The approach is illustrated with both simulated and real data and is shown to have appealing properties in comparison with both standard frequentist and Bayesian approaches