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Bayesian predictiveness, exchangeability and sufficientness in bacterial taxonomy
Department of Mathematics, University of Turku, 20014 Turku, Finland.
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
2002 (English)In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 177-178, 161-184 p.Conference paper, Published paper (Other academic)
Abstract [en]

We present a theory of classification and predictive identification of bacteria. Bacterial strains are characterized by a binary vector and the taxonomy is specified by attaching a label to each vector. The theory is developed from only two basic assumptions, viz. that the sequence of pairs of feature vectors and the attached labels is judged (infinitely) exchangeable and predictively sufficient. We derive expressions for the training error and the probability of identification error and show that latter is an affine function of the former. We prove the law of large numbers for identification matrices, which contain the fundamental information of bacterial data. We prove the Bayesian risk consistency of the predictive identification rule given by the theory and show that the training error is a consistent estimate of the generalization error. © 2002 Published by Elsevier Science Inc.

Place, publisher, year, edition, pages
2002. Vol. 177-178, 161-184 p.
Keyword [en]
Bahadur-Lazarsfeld expansions, Bayesian risk consistency, Multivariate Bernoulli distributions, Multivariate binary data, Supervised learning
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-47014DOI: 10.1016/S0025-5564(01)00096-7OAI: oai:DiVA.org:liu-47014DiVA: diva2:267910
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-13

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Koski, Timo

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