Chapter 17
Decision Theory
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Decision Theory
17.1 Bayes’ Theorem
17.2 Introduction to Decision Theory
17.3 Decision Making Using Posterior
Probabilities
17.4 Introduction to Utility Theory
17-2
Bayes’ Theorem
S1, S2, …, Sk represents k mutually exclusive possible states of nature,
one of which must be true
P(S1), P(S2), …, P(Sk) represents the prior probabilities of the k
possible states of nature
If E is a particular outcome of an experiment designed to determine
which is the true state of nature, then the posterior (or revised)
probability of a state Si, given the experimental outcome E, is:
P(Si  E)
P(Si|E) =
P(E)
P(Si )P(E|S i )

P(E)
P(Si )P(E|S i )

P(S1 )P(E|S1 )+P(S 2 )P(E|S 2 )+ ...+P(Sk )P(E|S k )
17-3
Introduction to Decision Theory
• States of nature: Set of potential future
conditions that affects decision results
• Alternatives: Set of alternative actions for the
decision maker to chose from
• Payoffs: Set of payoffs for each alternative under
each potential state of nature
• Often summarized in a payoff table
17-4
Decision Making Under Uncertainty
• Maximin: Identify the minimum (or worst) possible
payoff for each alternative and select the
alternative that maximizes the worst possible
payoff
• Pessimistic
• Maximax: Identify the maximum (or best) possible
payoff for each alternative and select the
alternative that maximizes the best possible payoff
• Optimistic
Expected value criterion: Using prior probabilities
for the states of nature, compute the expected
payoff for each alternative and select the
alternative with the largest expected payoff
17-5
Decision Making Using Posterior
Probabilities
• When we use expected value to choose the best
alternative, we call this prior decision analysis
• Often, sample information can be obtained to help
us make a better decision
• In this case, we compute expected values by
using posterior probabilities
• We call this posterior decision analysis
17-6
Introduction to Utility Theory
Utilities are measures of the relative value of varying dollar payoffs
for an individual decision maker and thus capture the decision
maker’s attitude toward risk. Under certain mild assumptions about
rational behavior, decision makers should replace dollar payoffs with
their respective utilities and maximize expected utility
Example Utility Curves
17-7