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Amenability: A survey for statistical applications of hunt-stein and related conditions on groups

  • James V. Bondar
  • Paul Milnes
Article

Summary

A number of conditions on groups have appeared in the literature of invariant statistical models in connection with minimaxity, approximation of invariant Bayes priors by proper priors, the relationship between Bayesian and classical inference, ergodic theorems, and other matters. In the last decade, rapid development has occurred in the field and many of these conditions are now known to be equivalent. We survey the subject, make the equivalences explicit, and list some groups of statistical interest which do, and also some which do not, have these properties. In particular, it is shown that the existence of the asymptotically invariant sequence of probabilities in the hypothesis of the Hunt-Stein theorem is equivalent to amenability, a condition that has been much studied by functional analysts.

Keywords

Statistical Model Stochastic Process Probability Theory Rapid Development Mathematical Biology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • James V. Bondar
    • 1
  • Paul Milnes
    • 1
  1. 1.Dept. of MathematicsUniversity of Western OntarioLondonCanada

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