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Representation insensitivity in immediate prediction under exchangeability

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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.
Keywords
coherence, imprecise probabilities, representation insensitivity, Johnson's sufficientness postulate, exchangeability, lower prevision, Rule of Succession, immediate prediction, Predictive inference, Imprecise Dirichlet-Multinomial Model, Representation Invariance Principle

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Chicago
De Cooman, Gert, Enrique Miranda, and Erik Quaeghebeur. 2009. “Representation Insensitivity in Immediate Prediction Under Exchangeability.” Ed. Jean-Marc Bernard. International Journal of Approximate Reasoning 50 (2): 204–216.
APA
De Cooman, Gert, Miranda, E., & Quaeghebeur, E. (2009). Representation insensitivity in immediate prediction under exchangeability. (J.-M. Bernard, Ed.)International Journal of Approximate Reasoning, 50(2), 204–216.
Vancouver
1.
De Cooman G, Miranda E, Quaeghebeur E. Representation insensitivity in immediate prediction under exchangeability. Bernard J-M, editor. International Journal of Approximate Reasoning. New York ; UNITED STATES: ELSEVIER SCIENCE INC; 2009;50(2):204–16.
MLA
De Cooman, Gert, Enrique Miranda, and Erik Quaeghebeur. “Representation Insensitivity in Immediate Prediction Under Exchangeability.” Ed. Jean-Marc Bernard. International Journal of Approximate Reasoning 50.2 (2009): 204–216. Print.
@article{497890,
  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.},
  author       = {De Cooman, Gert and Miranda, Enrique and Quaeghebeur, Erik},
  editor       = {Bernard, Jean-Marc},
  issn         = {0888-613X},
  journal      = {International Journal of Approximate Reasoning},
  keyword      = {coherence,imprecise probabilities,representation insensitivity,Johnson's sufficientness postulate,exchangeability,lower prevision,Rule of Succession,immediate prediction,Predictive inference,Imprecise Dirichlet-Multinomial Model,Representation Invariance Principle},
  language     = {eng},
  number       = {2},
  pages        = {204--216},
  publisher    = {ELSEVIER SCIENCE INC},
  title        = {Representation insensitivity in immediate prediction under exchangeability},
  url          = {http://dx.doi.org/10.1016/j.ijar.2008.03.010},
  volume       = {50},
  year         = {2009},
}

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