Representation insensitivity in immediate prediction under exchangeability

Gert de Cooman, Enrique Miranda, Erik Quaeghebeur

Research output: Contribution to journalArticleAcademicpeer-review

14 Citations (Scopus)

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. 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.

Original languageEnglish
Pages (from-to)204-216
Number of pages13
JournalInternational Journal of Approximate Reasoning
Volume50
Issue number2
DOIs
Publication statusPublished - Feb 2009
Externally publishedYes

Keywords

  • Coherence
  • Exchangeability
  • Immediate prediction
  • Imprecise Dirichlet-Multinomial Model
  • Imprecise probabilities
  • Johnson's sufficientness postulate
  • Lower prevision
  • Predictive inference
  • Representation insensitivity
  • Representation invariance principle
  • Rule of Succession

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