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Faculty Mentor

Danica M. Ommen, Cedric Neumann, Christopher P. Saunders

Abstract

Forensic evidence is often an important factor in criminal investigations. Analyzing evidence in an objective way involves the use of statistics. However, many evidence types (i.e., glass fragments, fingerprints, shoe impressions) are very complex. This makes the use of statistical methods, such as model selection in Bayesian inference, extremely difficult.

Approximate Bayesian Computation is an algorithmic method in Bayesian analysis that can be used for model selection. It is especially useful because it can be used to assign a Bayes Factor without the need to directly evaluate the exact likelihood function - a difficult task for complex data. Several criticisms of ABC (specifically when used for model choice) can be found in the literature, yet the potential benefits of the method warrant study of the performance under controlled situations. This paper explores the use of ABC in forensic science through use of a glass example. The ABC approximation of the Bayes Factor provided the correct direction of support in the majority of known cases in the glass example. However, the approximations did not agree with the weight of support given by analytical Bayes Factors. Exploration of the inconsistent portion of results uncovered an issue with the method used to choose a threshold value in ABC. A novel method, based on a relationship between the ABC Bayes Factor and the Receiver Operating Characteristic curve, was developed to address this issue. This method produced more stable results than the traditional ABC methodology.

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