Hostname: page-component-5c6d5d7d68-vt8vv Total loading time: 0.001 Render date: 2024-08-16T08:22:23.886Z Has data issue: false hasContentIssue false
  • English
  • Français

Mixture catastrophes and Bayes decision theory

Published online by Cambridge University Press:  24 October 2008

J. Q. Smith
J. Q. Smith
Affiliation:
University College, London
Get access Rights & Permissions [Opens in a new window]

Extract

To make a Bayes decision we choose the infimum of an expected loss function. Catastrophe theory classifies a wide class of functions locally in terms of their critical values. Firstly we will show how this local classification relates globally to some mixtures of symmetric expected loss functions. Secondly we shall indicate how such mixtures can arise and how the above classification can be usefully applied to the qualitative study of the behaviour of a Bayes decision-maker.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 86 , Issue 1 , July 1979 , pp. 91 - 101
Copyright
Copyright © Cambridge Philosophical Society 1979

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Billingsley, P.Convergence of probability measures (McGraw-Hill, 1972).Google Scholar
(2)De Groot, M. H.Optimal statistical decisions (McGraw-Hill, 1970).Google Scholar
(3)Harrison, P. J. and Stevens, C. F. Bayesian forecasting (with discussion). J. Roy. Statist. Soc. Ser. B. 38 (1976) 206–247.Google Scholar
(4)Isnard, C. A. and Zeeman, E. C.Some models from catastrophe theory in the social sciences Catastrophe theory selected papers 1972–1977 E. C. Zeeman (Addison-Wesley, 1977), pp. 303–359.Google Scholar
(5)Lindley, D. V.A class of utility functions. Ann. Statist. 4 (1976), 1–10.Google Scholar
(6)Smith, J. Q. Problems in Bayesian statistics relating to discontinuous phenomena, catastrophe theory and forecasting. Ph.D. thesis, University of Warwick, 1978.Google Scholar
(7)Smith, J. Q., Harrison, P. J. and Zeeman, E. C.The analysis of some discontinuous decision processes (to appear).Google Scholar