期刊
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
卷 50, 期 2, 页码 204-216出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.ijar.2008.03.010
关键词
Predictive inference; Immediate prediction; Rule of Succession; Lower prevision; Imprecise probabilities; Coherence; Exchangeability; Representation invariance principle; Representation insensitivity; Imprecise Dirichlet-Multinomial Model; Johnson's sufficientness postulate
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. We establish that such representation insensitive predictive models have very interesting properties, and show that among such models, the ones produced by the Imprecise Dirichlet-Multinomial Model are quite special in a number of ways. In the Conclusion, we discuss the open question as to how unique the predictive lower previsions of the Imprecise Dirichlet-Multinomial Model are in being representation insensitive. (C) 2008 Elsevier Inc. All rights reserved.
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