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Imprecise probability models for inference in exponential families

Erik Quaeghebeur (UGent) and Gert de Cooman (UGent)
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Abstract
When considering sampling models described by a distribution from an exponential family, it is possible to create two types of imprecise probability models. One is based on the corresponding conjugate distribution and the other on the corresponding predictive distribution. In this paper, we show how these types of models can be constructed for any (regular, linear, canonical) exponential family, such as the centered normal distribution. To illustrate the possible use of such models, we take a look at credal classification. We show that they are very natural and potentially promising candidates for describing the attributes of a credal classifier, also in the case of continuous attributes.
Keywords
Exponential family, Inference, Imprecise probability models, Conjugate analysis, Naive credal classifier

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MLA
Quaeghebeur, Erik, and Gert de Cooman. “Imprecise Probability Models for Inference in Exponential Families.” ISIPTA 05-PROCEEDINGS OF THE FOURTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITIES AND THEIR APPLICATIONS, edited by Fabio G Cozman et al., International Society for Imprecise Probability: Theories and Applications (SIPTA), 2005, pp. 287–96.
APA
Quaeghebeur, E., & de Cooman, G. (2005). Imprecise probability models for inference in exponential families. In F. G. Cozman, R. Nau, & T. Seidenfeld (Eds.), ISIPTA 05-PROCEEDINGS OF THE FOURTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITIES AND THEIR APPLICATIONS (pp. 287–296). Manno, Switzerland: International Society for Imprecise Probability: Theories and Applications (SIPTA).
Chicago author-date
Quaeghebeur, Erik, and Gert de Cooman. 2005. “Imprecise Probability Models for Inference in Exponential Families.” In ISIPTA 05-PROCEEDINGS OF THE FOURTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITIES AND THEIR APPLICATIONS, edited by Fabio G Cozman, Robert Nau, and Teddy Seidenfeld, 287–96. Manno, Switzerland: International Society for Imprecise Probability: Theories and Applications (SIPTA).
Chicago author-date (all authors)
Quaeghebeur, Erik, and Gert de Cooman. 2005. “Imprecise Probability Models for Inference in Exponential Families.” In ISIPTA 05-PROCEEDINGS OF THE FOURTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITIES AND THEIR APPLICATIONS, ed by. Fabio G Cozman, Robert Nau, and Teddy Seidenfeld, 287–296. Manno, Switzerland: International Society for Imprecise Probability: Theories and Applications (SIPTA).
Vancouver
1.
Quaeghebeur E, de Cooman G. Imprecise probability models for inference in exponential families. In: Cozman FG, Nau R, Seidenfeld T, editors. ISIPTA 05-PROCEEDINGS OF THE FOURTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITIES AND THEIR APPLICATIONS. Manno, Switzerland: International Society for Imprecise Probability: Theories and Applications (SIPTA); 2005. p. 287–96.
IEEE
[1]
E. Quaeghebeur and G. de Cooman, “Imprecise probability models for inference in exponential families,” in ISIPTA 05-PROCEEDINGS OF THE FOURTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITIES AND THEIR APPLICATIONS, Pittsburgh, PA, USA, 2005, pp. 287–296.
@inproceedings{320871,
  abstract     = {{When considering sampling models described by a distribution from an exponential family, it is possible to create two types of imprecise probability models. One is based on the corresponding conjugate distribution and the other on the corresponding predictive distribution. In this paper, we show how these types of models can be constructed for any (regular, linear, canonical) exponential family, such as the centered normal distribution.
To illustrate the possible use of such models, we take a look at credal classification. We show that they are very natural and potentially promising candidates for describing the attributes of a credal classifier, also in the case of continuous attributes.}},
  author       = {{Quaeghebeur, Erik and de Cooman, Gert}},
  booktitle    = {{ISIPTA 05-PROCEEDINGS OF THE FOURTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITIES AND THEIR APPLICATIONS}},
  editor       = {{Cozman, Fabio G and Nau, Robert and Seidenfeld, Teddy}},
  keywords     = {{Exponential family,Inference,Imprecise probability models,Conjugate analysis,Naive credal classifier}},
  language     = {{eng}},
  location     = {{Pittsburgh, PA, USA}},
  pages        = {{287--296}},
  publisher    = {{International Society for Imprecise Probability: Theories and Applications (SIPTA)}},
  title        = {{Imprecise probability models for inference in exponential families}},
  url          = {{http://www.sipta.org/isipta05/proceedings/019.html}},
  year         = {{2005}},
}

Web of Science
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