7. Decision Functions

  1. Giovanni Parmigiani1 and
  2. Lurdes Y. T. Inoue2

Published Online: 1 DEC 2010

DOI: 10.1002/9780470746684.ch7

Decision Theory

Decision Theory

How to Cite

Parmigiani, G. and Inoue, L. Y. T. (2009) Decision Functions, in Decision Theory, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470746684.ch7

Author Information

  1. 1

    Johns Hopkins University, Baltimore, USA

  2. 2

    University of Washington, Seattle, USA

Publication History

  1. Published Online: 1 DEC 2010
  2. Published Print: 17 APR 2009

Book Series:

  1. Wiley Series in Probability and Statistics

Book Series Editors:

  1. Walter A. Shewhart and
  2. Samuel S. Wilks

ISBN Information

Print ISBN: 9780471496571

Online ISBN: 9780470746684



  • decision functions;
  • architecture of statistical decision theory;
  • statistician - choosing among a set of actions, whose consequences depend on some unknown state of the world, or state of nature;
  • loss function and estimation;
  • expected utility principle applying to expected losses;
  • data-based decisions;
  • rationality principles and likelihood principle;
  • travel insurance example;
  • randomized decision rules;
  • classification and hypothesis tests


This chapter contains sections titled:

  • Basic concepts

  • Data-based decisions

  • The travel insurance example

  • Randomized decision rules

  • Classification and hypothesis tests

  • Estimation

  • Minimax–Bayes connections

  • Exercises