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A Two-Level Model for Evidence Evaluation in the Presence of Zeros

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Likelihood ratios (LRs) provide a natural way of computing the value of evidence under competing propositions. We propose LR models for classification and comparison that extend the ideas of Aitken, Zadora, and Lucy and Aitken and Lucy to include consideration of zeros. Instead of substituting zeros by a small value, we view the presence of zeros as informative and model it using Bernoulli distributions. The proposed models are used for evaluation of forensic glass (comparison and classification problem) and paint data (comparison problem). Two hundred and sixty-four glass samples were analyzed by scanning electron microscopy, coupled with an energy dispersive X-ray spectrometer method and 36 acrylic topcoat paint samples by pyrolysis gas chromatography hyphened with mass spectrometer method. The proposed LR model gave very satisfactory results for the glass comparison problem and for most of the classification tasks for glass. Results of comparison of paints were also highly satisfactory, with only 3.0% false positive answers and 2.8% false negative answers.
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Keywords: evidence evaluation; forensic science; graphical models; likelihood ratio; missing data; multivariate data

Document Type: Research Article

Affiliations: 1: Institute of Forensic Research, Westerplatte 9, PL-31-033 Krakow, Poland. 2: Department of Statistics, University of Glasgow, 15 University Gardens, Glasgow G12 8QW, U.K. 3: School of Mathematics and The Joseph Bell Centre for Forensic Statistics and Legal Reasoning, The King’s Buildings, The University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, U.K.

Publication date: March 1, 2010

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