Marginalization Paradoxes in Bayesian and Structural Inference

Dawid, A. P.; Stone, M.; Zidek, James V.

doi:10.1111/j.2517-6161.1973.tb00952.x

Cited by 202 publications

(120 citation statements)

References 25 publications

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“…One can see that in refs. [9,[18][19][20][30][31]. Therefore Definition 5 is applied to the situation in which the fiducial inferences have a frequentist meaning, such as the regular parametric function given in Definition 6.…”

Section: Marginal Fiducial Distributionsmentioning

confidence: 99%

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Fiducial inference in the pivotal family of distributions

2006

SCI CHINA SER A

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In this paper a family, called the pivotal family, of distributions is considered. A pivotal family is determined by a generalized pivotal model. Analytical results show that a great many parametric families of distributions are pivotal. In a pivotal family of distributions a general method of deriving fiducial distributions of parameters is proposed. In the method a fiducial model plays an important role. A fiducial model is a function of a random variable with a known distribution, called the pivotal random element, when the observation of a statistic is given. The method of this paper includes some other methods of deriving fiducial distributions. Specially the first fiducial distribution given by Fisher can be derived by the method. For the monotone likelihood ratio family of distributions, which is a pivotal family, the fiducial distributions have a frequentist property in the Neyman-Pearson view. Fiducial distributions of regular parametric functions also have the above frequentist property. Some advantages of the fiducial inference are exhibited in four applications of the fiducial distribution. Many examples are given, in which the fiducial distributions cannot be derived by the existing methods.

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Section: Marginal Fiducial Distributionsmentioning

confidence: 99%

“…Many discussions on them, including some controversies, can be found in refs. [11][12][13][14][15][16][17][18][19][20][21][22][23]. The views of Efron [24] about the fiducial inference should be noted.…”

Section: Introductionmentioning

confidence: 99%

Fiducial inference in the pivotal family of distributions

2006

SCI CHINA SER A

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“…Some references on these critical issues are Berger et al (1988), Dawid et al (1973) and Regazzini (1983, pp. 83-97).…”

Section: Some Noninfonnative Priorsmentioning

confidence: 99%

Probability matching priors: a review

Scricciolo

1999

J. Ital. Statist. Soc.

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“…However, the prior distribution has a problem with it which is too subjective [20]. To compensate, studies of noninformative prior distribution have been carried out and applied to situations where information is lacking.…”

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confidence: 98%