W. E. Johnson's "Sufficientness" Postulate

Zabell, Sandy L.

doi:10.1214/aos/1176345975

Cited by 114 publications

(62 citation statements)

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“…Carnap showed that his conditions are equivalent to statement (i) in Theorem 3.4 (see for instance Zabell, 1981). This, together with the just derived observations, gives an alternative proof for our Theorem 3.4.…”

Section: The Translation Algorithm Of Sectionmentioning

confidence: 59%

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Surveys in Game Theory and Related Topics.

Baston

1988

Journal of the Royal Statistical Society. Series A (Statistics

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Section: The Translation Algorithm Of Sectionmentioning

confidence: 59%

“…The results of section 3 were obtained by translating work of Carnap on inductive reasoning, see Carnap (1962), Carnap & Jeffrey (1971) Zabell (1981). As an example let us suppose that a die has been thrown several times.…”

Section: The Translation Algorithm Of Sectionmentioning

confidence: 99%

Surveys in Game Theory and Related Topics.

Baston

1988

Journal of the Royal Statistical Society. Series A (Statistics

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“…where the hyperparameter λ cjl > 0, for all index values (see Zabell 1982). Under this result, the so called sufficientness postulate, the explicit predictive probability mass function for the items equals…”

Section: Model-based Unsupervised Predictive Classificationmentioning

confidence: 97%

Bayesian unsupervised classification framework based on stochastic partitions of data and a parallel search strategy

Corander

Gyllenberg

Koski

2009

Adv Data Anal Classif

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Advantages of statistical model-based unsupervised classification over heuristic alternatives have been widely demonstrated in the scientific literature. However, the existing model-based approaches are often both conceptually and numerically instable for large and complex data sets. Here we consider a Bayesian model-based method for unsupervised classification of discrete valued vectors, that has certain advantages over standard solutions based on latent class models. Our theoretical formulation defines a posterior probability measure on the space of classification solutions corresponding to stochastic partitions of observed data. To efficiently explore the classification space we use a parallel search strategy based on non-reversible stochastic processes. A decision-theoretic approach is utilized to formalize the inferential process in the context of unsupervised classification. Both real and simulated data sets are used for the illustration of the discussed methods.

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“…Thus, the Pólya's urn scheme characterizes the conjugate family of Dirichlet prior distributions for a multinomial statistical model. A characterization based on Johnson's predictive sufficiency postulate is given by Zabell [28] .…”

Section: Pólya Urn Schemementioning

confidence: 99%

Predictive Distribution (de Finetti's View)

Fortini

Petrone

2016

Wiley StatsRef: Statistics Reference Online

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Abstract:In Bayesian statistics, the "predictive distribution" is defined as the conditional distribution of future observations, given past observations. The predictive approach to inference highlights the centrality of predictive distributions, both for model assignment and inference. The relevance of the predictive approach is twofold. Starting from de Finetti, it is a cornerstone of the philosophical foundation of Bayesian statistics. Moreover, it has shown to be extremely fruitful, for model construction, in research areas with strong applied motivation, such as Bayesian nonparametrics and machine learning.

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W. E. Johnson's "Sufficientness" Postulate

Cited by 114 publications

References 0 publications

Surveys in Game Theory and Related Topics.

Surveys in Game Theory and Related Topics.

Bayesian unsupervised classification framework based on stochastic partitions of data and a parallel search strategy

Predictive Distribution (de Finetti's View)

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