Identification of taxon through classification with partial reject options

• Published in: Journal of the Royal Statistical Society Series C: Applied Statistics Vol. 72; no. 4; pp. 937 - 975
• Main Authors: Karlsson, Måns, Hössjer, Ola
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 02.09.2023
• Subjects: Bayesian analysis; Bayesian classification; Birds; Classification; classification with covariates; Clustering; Datasets; Discriminant analysis; Machine learning; matematisk statistik; Mathematical Statistics; Normal distribution; partial observations; set-valued classifiers; species identification; Statistical analysis; statistical ornithology; Supervised learning; Uncertainty
• ISSN: 0035-9254; 1467-9876; 1467-9876
• DOI: 10.1093/jrsssc/qlad036

Identification of taxa can significantly be assisted by statistical classification based on trait measurements either individually or by phylogenetic (clustering) methods. In this article, we present a general Bayesian approach for classifying species individually based on measurements of a mixture of continuous and ordinal traits, and any type of covariates. The trait vector is derived from a latent variable with a multivariate Gaussian distribution. Decision rules based on supervised learning are presented that estimate model parameters through blocked Gibbs sampling. These decision regions allow for uncertainty (partial rejection), so that not necessarily one specific category (taxon) is output when new subjects are classified, but rather a set of categories including the most probable taxa. This type of discriminant analysis employs reward functions with a set-valued input argument, so that an optimal Bayes classifier can be defined. We also present a way of safeguarding against outlying new observations, using an analogue of a p-value within our Bayesian setting. We refer to our Bayesian set-valued classifier as the Karlsson–Hössjer method, and it is illustrated on an original ornithological data set of birds. We also incorporate model selection through cross-validation, exemplified on another original data set of birds.