Typicality and predictive distributions in discriminant function analysis

Lyle W. Konigsberg, Susan R. Frankenberg

Research output: Contribution to journalArticlepeer-review


While discriminant function analysis is an inherently Bayesian method, researchers attempting to estimate ancestry in human skeletal samples often follow discriminant function analysis with the calculation of frequentist-based typicalities for assigning group membership. Such an approach is problematic because it fails to account for admixture and for variation in why individuals may be classifijied as outliers or nonmembers of particular groups. This article presents an argument and methodology for employing a fully Bayesian approach in discriminant function analysis applied to cases of ancestry estimation. The approach requires adding the calculation, or estimation, of predictive distributions as the fijinal step in ancestry-focused discriminant analyses. The methods for a fully Bayesian multivariate discriminant analysis are illustrated using craniometrics from identifijied population samples within the Howells published data. The article also presents ways to visualize predictive distributions calculated in more than three dimensions, explains the limitations of typicality measures, and suggests an analytical route for future studies of ancestry and admixture based in discriminant function analysis.

Original languageEnglish (US)
Pages (from-to)31-44
Number of pages14
JournalHuman biology
Issue number1
StatePublished - Dec 1 2018


  • Admixture
  • Bayesian analysis
  • Outliers
  • Posterior probability
  • Tukey depth

ASJC Scopus subject areas

  • General Medicine


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