Calculation of likelihood ratios for inference of biological sex from human skeletal remains

Abstract It is common in forensic anthropology to draw inferences (e.g., inferences with respect to biological sex of human remains) using statistical models applied to anthropometric data. Commonly used models can output posterior probabilities, but a threshold is usually applied in order to obtain a classification. In the forensic-anthropology literature, there is some unease with this “fall-off-the-cliff” approach. Proposals have been made to exclude results that fall within a “zone of uncertainty”, e.g., if the posterior probability for “male” is greater than 0.95 then the remains are classified as male, and if the posterior probability for “male” is less than 0.05 then the remains are classified as female, but if the posterior probability for “male” is between 0.05 and 0.95 the remains are not classified as either male or female. In the present paper, we propose what we believe is a simpler solution that is in line with interpretation of evidence in other branches of forensic science: implementation of the likelihood-ratio framework using relevant data, quantitative measurements, and statistical models. Statistical models that can implement this approach are already widely used in forensic anthropology. All that is required are minor modifications in the way those models are used and a change in the way practitioners and researchers think about the meaning of the output of those models. We explain how to calculate likelihood ratios using osteometric data and linear discriminant analysis, quadratic discriminant analysis, and logistic regression models. We also explain how to empirically validate likelihood-ratio models.