Advertisement

Statistical Decision Theory

  • James O. Berger
Part of the The New Palgrave book series (NPA)

Abstract

Decision theory is the science of making optimal decisions in the face of uncertainty. Statistical decision theory is concerned with the making of decisions when in the presence of statistical knowledge (data) which sheds light on some of the uncertainties involved in the decision problem. The generality of these definitions is such that decision theory (dropping the qualifier ‘statistical’ for convenience) formally encompasses an enormous range of problems and disciplines. Any attempt at a general review of decision theory is thus doomed; all that can be done is to present a description of some of the underlying ideas.

Keywords

Utility Function Decision Rule Decision Problem Prior Information Decision Theory 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. Bayes, T. 1763. An essay towards solving a problem in the doctrine of changes. Philosophical Transactions of the Royal Society, London 53, 370–418.CrossRefGoogle Scholar
  2. Berger, J. 1985. Statistical Decision Theory and Bayesian Analysis. New York: Springer-Verlag.CrossRefGoogle Scholar
  3. Blackwell, D. and Girshick, M.A. 1954. Theory of Games and Statistical Decisions. New York: Wiley.Google Scholar
  4. De Groot, M.H. 1970. Optimal Statistical Decisions. New York: McGraw-Hill.Google Scholar
  5. Ferguson, T.S. 1967. Mathematical Statistics: A Decision Theoretic Approach. New York: Academic Press.Google Scholar
  6. Fishburn, P.C. 1981. Subjective expected utility: a review of normative theories. Theory and Decision 13, 139–99.CrossRefGoogle Scholar
  7. Neyman, J. 1977. Frequentist probability and frequentist statistics. Synthese 36, 97–131.CrossRefGoogle Scholar
  8. Neyman, J. and Pearson, E.S. 1933. On the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Society, London, 231–289–337.Google Scholar
  9. Raiffa, H. 1968. Decision Analysis: Introductory Lectures on Choices under Uncertainty. Reading, Mass.: Addison-Wesley.Google Scholar
  10. Raiffa, H. and Schlaifer, R. 1961. Applied Statistical Decision Theory. Boston: Division of Research, Graduate School of Business Administration, Harvard University.Google Scholar
  11. Ramsey, F.P. 1931. Truth and probability. In The Foundations of Mathematics and Other Logical Essays, London: Kegan, Paul, Trench and Trubner.Google Scholar
  12. Reprinted in Studies in Subjective Probability, ed. H. Kyburg and H. Smokier, New York: Wiley, 1964, 61–92.Google Scholar
  13. Savage, L.J. 1954. The Foundations of Statistics. New York: Wiley.Google Scholar
  14. Wald, A. 1950. Statistical Decision Functions. New York: Wiley.Google Scholar
  15. Winkler, R.L. 1972. An Introduction to Bayesian Inference and Decision. New York: Holt, Rinehart & Winston.Google Scholar

Copyright information

© Palgrave Macmillan, a division of Macmillan Publishers Limited 1990

Authors and Affiliations

  • James O. Berger

There are no affiliations available

Personalised recommendations