On Bayes procedures

Lorraine Schwartz

doi:10.1007/BF00535479

Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete

March 1965, Volume 4, Issue 1, pp 10–26

On Bayes procedures

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Lorraine Schwartz

Article

Received:: 16 March 1964

DOI: 10.1007/BF00535479

Cite this article as:: Schwartz, L. Z. Wahrscheinlichkeitstheorie verw Gebiete (1965) 4: 10. doi:10.1007/BF00535479

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Summary

A result of Doob regarding consistency of Bayes estimators is extended to a large class of Bayes decision procedures in which the loss functions are not necessarily convex. Rather weak conditions are given under which the Bayes procedures are consistent. One set involves restrictions on the a priori distribution and follows an example in which the choice of a priori distribution determines whether the Bayes estimators are consistent. Another example shows that the maximum likelihood estimators may be consistent when the Bayes estimators are not. However, the conditions given are of an essentially weaker nature than those established for consistency of maximum likelihood estimators.

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Lorraine Schwartz
- 1

1.Dept. of MathematicsUniversity of British ColumbiaVancouver 8Canada

On Bayes procedures

Summary

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