Rebecca Baker, Pauline Coolen-Schrijner, Frank Coolen, Thomas Augustin

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Nonparametric predictive inference for subcategory data

Abstract

Nonparametric predictive inference (NPI) is a framework for statistical inference in the absence of prior knowledge. We present NPI for multinomial data with subcategories, motivated by the hierarchical structure of many multinomial data sets. We consider situations with known and with unknown numbers of subcategories, and present lower and upper probabilities for general events involving one future observation. We present properties of the model and an algorithm to derive an approximation to the maximum entropy distribution.

Keywords

classification, multinomial data, nonparametric predictive inference, subcategories

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Authors’ addresses

Rebecca Baker
14 Stafford Road
Gretton
Northamptonshire
NN17 3DP

Pauline Coolen-Schrijner

Frank Coolen
Department of Mathematical Sciences
Science Laboratories, South Road
Durham, DH1 3LE,
England

Thomas Augustin
Department of Statistics
University of Munich
Ludwigstr. 33
D-80539 Munich
Germany

E-mail addresses

Rebecca Baker		r.m.baker@dunelm.org.uk
Pauline Coolen-Schrijner
Frank Coolen		Frank.Coolen@durham.ac.uk
Thomas Augustin		thomas@stat.uni-muenchen.de