FOURTH INTERNATIONAL SYMPOSIUM ON
IMPRECISE PROBABILITIES AND THEIR APPLICATIONS
Carnegie Mellon University
Pittsburgh, PA, USA
July 20-23 2005

ISIPTA'05 ELECTRONIC PROCEEDINGS

Frank Coolen, Thomas Augustin

Learning from multinomial data: a nonparametric predictive alternative to the Imprecise Dirichlet Model

Abstract

A new model for learning from multinomial data has recently been developed, giving predictive inferences in the form of lower and upper probabilities for a future observation. Apart from the past observations, no information on the sample space is assumed, so explicitly no assumptions are made on the number of possible categories. In this paper, we briefly present the general lower and upper probabilities corresponding to this model, and illustrate their properties via two examples taken from Walley's paper which introduced the imprecise Dirichlet model (IDM). As our approach is nonparametric, its applicability is more restricted. However, our inferences do not suffer from some disadvantages of the IDM.

Keywords. Imprecise Dirichlet model, imprecise probabilities, interval probability, multinomial data, nonparametric predictive inference, probability wheel

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Authors addresses:

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:

Frank Coolen Frank.Coolen@durham.ac.uk
Thomas Augustin thomas@stat.uni-muenchen.de


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