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:
| Gert De Cooman | gert.decooman@ugent.be |
| Enrique Miranda | enrique.miranda@urjc.es |
| Erik Quaeghebeur | Erik.Quaeghebeur@UGent.be |