Stature estimation and calibration: Bayesian and maximum likelihood perspectives in physical anthropology

Many applied problems in physical anthropology involve estimation of an unobservable quantity (such as age at death or stature) from quantities that are observable. Two of the more disparate subdisciplines of our discipline, paleoanthropology and forensic anthropology, routinely make use of various estimation methods on a case-by-case basis. We discuss the rationales for making estimations on isolated cases, taking stature estimation from femoral and humerus lengths as an example. We show that the entirety of our discussion can be placed within the context of calibration problems, where a large calibration sample is used to estimate an unobservable quantity for a single skeleton. Taking a calibration approach to the problem highlights the essentially Bayesian versus maximum likelihood nature of the question of stature estimation. On the basis of both theoretical arguments and practical examples, we show that inverse calibration (regression of stature on bone length) is generally preferred when the stature distribution for a reference sample forms a reasonable prior, while classical calibration (regression of bone length on stature followed by solving for stature) is preferred when there is reason to suspect that the estimated stature will be an extrapolation beyond the useful limits of the reference sample statures. The choice between these two approaches amounts to the decision to use either a Bayesian or a maximum likelihood method.