Bayesian Decision Analysis

Synonyms

Bayesian; Decision theory

Definition

Bayesian decision analysis (Smith 2010) is concerned with making choices when the outcomes cannot be predicted with certainty. Probabilities are assigned to the various possible outcomes and so to values of the reward or payoff, under each possible choice. We choose between probability distributions of rewards. This is done by making the choice which maximizes the expected utility (utility function), that is, by choosing the alternative which gives the probability distribution of rewards with the greatest expectation of utility, where utility is a function of the reward. For example, suppose that a person’s utility for small financial rewards is an increasing linear function of the monetary value. Suppose that this person is given the choice between alternatives A and B with reward distributions as follows:

• A: $1 with probability 0.6 or $2 with probability 0.4

• B: $0 with probability 0.2 or $2 with probability 0.8

The optimal choice is then...