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ArticleOriginal scientific text

Title

Sufficiency in bayesian models

Authors 1, 1

Affiliations

  1. Institute of Applied Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

Abstract

We consider some fundamental concepts of mathematical statistics in the Bayesian setting. Sufficiency, prediction sufficiency and freedom can be treated as special cases of conditional independence. We give purely probabilistic proofs of the Basu theorem and related facts.

Keywords

ENG
sufficiency, connditional independence, Bayesian models, prediction sufficiency, freedom

Bibliography

  1. J. R. Barra (1971), Notions fondamentales de statistique mathématique, Dunod, Paris.
  2. D. Basu (1953), On statistics independent of a complete sufficient statistic, Sankhyā 15, 377-380 and 20 (1958), 223-226.
  3. Y. S. Chow and H. Teicher (1988), Probability Theory. Independence, Interchangeability, Martingales, Springer.
  4. K. R. Parthasarathy (1980), Introduction to Probability and Measure.
  5. K. Takeuchi and M. Takahira (1975), Characterizations of prediction sufficiency (adequacy) in terms of risk functions, Ann. Statist. 3, 1018-1024.
  6. E. N. Torgensen (1977), Prediction sufficiency when the loss function does not depend on the unknown parameter, ibid. 5, 155-163.
Applicationes Mathematicae
1998-1999/25/1
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Pages:
113-120
Main language of publication
English
Received
1997-05-14
Published
1998
Exact and natural sciences