An Overview of the Two-Stage, Score-Based Likelihood Ratio, and Bayes Factor Approaches for Writership Determinations

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Ommen, Danica
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Center for Statistics and Applications in Forensic Evidence
The Center for Statistics and Applications in Forensic Evidence (CSAFE) carries out research on the scientific foundations of forensic methods, develops novel statistical methods and transfers knowledge and technological innovations to the forensic science community. We collaborate with more than 80 researchers and across six universities to drive solutions to support our forensic community partners with accessible tools, open-source databases and educational opportunities.
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The Department of Statistics seeks to teach students in the theory and methodology of statistics and statistical analysis, preparing its students for entry-level work in business, industry, commerce, government, or academia.

The Department of Statistics was formed in 1948, emerging from the functions performed at the Statistics Laboratory. Originally included in the College of Sciences and Humanities, in 1971 it became co-directed with the College of Agriculture.

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A variety of statistical approaches have been developed at the Center for Statistics and Applications in Forensic Evidence (CSAFE) to address the question of writership for forensic document examinations. Previous work at CSAFE has addressed the closed-set problem, when the writer of a questioned document must be one out of a list of known writers. This presentation focuses on a set of evidence interpretation methods that can address the open-set problem, when the writer of a questioned document could be an unknown writer not included in the known list. To date, CSAFE has developed three types of statistical writership evaluation methods, a Two-Stage approach, a score-based likelihood ratio, and a Bayes Factor. All methods are demonstrated on a set of handwriting collected by CSAFE and features of the writing are extracted using the CSAFE-developed ‘handwriter’ R package. The key components of each method, as well as their strengths and weaknesses, will be described.

The Two-Stage approach begins with a comparison of the documents. If the writing features of the documents are similar (or dissimilar) enough to declare they were written by the same (or different) writer, then the significance of this determination is assessed via the random match (or nonmatch) probability.

Like the Two-Stage approach, the score-based likelihood ratio (SLR) method begins with a comparison of the documents resulting in a score. Then, two reference distributions are used to determine how often that score is seen among same-writer and different-writer pairs. The ratio of the density of the score in the same-writer versus the different-writer reference distribution is the desired SLR value.

Unlike the previous approaches, the Bayes Factor approach begins with statistical models for the writing features directly: representing the likelihood of observing the writing features given the “same-writer” or “different-writer” hypotheses. Both statistical models will have unknown parameter values. To represent a variety of possible values for the parameter, weighting more likely values higher and less likely values lower, we use a prior. Computational methods can then be used to compute the value of the Bayes Factor by combining the likelihood models with the priors.
This presentation is from Forensic Document Examiners Live INternational Knowledge Exchange on Documents (FDE Linked), Virtual Conference, March 2023. Posted with permission of CSAFE.