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ISIPTA'07 -
FIFTH INTERNATIONAL SYMPOSIUM ON

IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS

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Charles University, Faculty of Mathematicsand Physics

Prague, Czech Republic

16-19 July 2007

## ELECTRONIC PROCEEDINGS

## Gert De Cooman, Enrique Miranda, Erik Quaeghebeur

# Immediate prediction under exchangeability and representation insensitivity

### Abstract

We consider immediate predictive inference, where a subject, using a number of observations of a finite number of exchangeable random variables, is asked to coherently model his beliefs about the next observation, in terms of a predictive lower prevision. We study when such predictive lower previsions are representation insensitive, meaning that they are essentially independent of the choice of the (finite) set of possible values for the random variables. Such representation insensitive predictive models have very interesting properties, and among such models, the ones produced by the Imprecise Dirichlet-Multinomial Model are quite special in a number of ways.

** Keywords. ** Predictive inference, immediate prediction, lower prevision, imprecise probabilities, coherence, exchangeability, representation invariance, representation insensitivity, Imprecise Dirichlet-Multinomial Model, Johnson's sufficientness postulate.

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** Authors addresses: **

Gert De Cooman

Technologiepark - Zwijnaarde 914

9052 Zwijnaarde

Enrique Miranda

Dpto. de Informática, Estadística y Telemática

Univ. Rey Juan Carlos

C-Tulipán, s/n

Móstoles (Madrid)

SPAIN

Erik Quaeghebeur

Technologiepark-Zwijnaarde 914

9052 Zwijnaarde

** E-mail addresses: **

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