Romain Gauriot

Statistical Challenges in the Quantification of Gunshot Residue Evidence

The discharging of a gun results in the formation of extremely small particles known as gunshot residues (GSR). These may be deposited on the skin and clothing of the shooter, on other persons present, and on nearby items or surfaces. Several factors and their complex interactions affect the number of detectable GSR particles, which can deeply influence the conclusions drawn from likelihood ratios or posterior probabilities for prosecution hypotheses of interest. We present Bayesian network models for casework examples and demonstrate that probabilistic quantification of GSR evidence can be very sensitive to the assumptions concerning the model structure, prior probabilities, and the likelihood components. This finding has considerable implications for the use of statistical quantification of GSR evidence in the legal process.

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. Copyright

Nash at Wimbledon: Evidence from Half a Million Serves

Minimax and its generalization to mixed strategy Nash equilibrium is the cornerstone of our understanding of strategic situations that require decision makers to be unpredictable. Using a dataset of nearly half a million serves from over 3000 matches, we examine whether the behavior of professional tennis players is consistent with the Minimax Hypothesis. The large number of matches in our dataset requires the development of a novel statistical test, which we show is more powerful than the tests used in prior related studies. We find that win rates conform remarkably closely to the theory for men, but conform somewhat less neatly for women. We show that the behavior in the field of more highly ranked (i.e., better) players conforms more closely to theory.