This rather lengthy chapter provides an introduction to invariant decision problems. After describing the basic ingredients in a decision problem, invariance is introduced and used to define an invariant decision problem. A main result in this chapter shows how to construct a best invariant rule when the group action is transitive on the parameter space and when the dominating measure is decomposable [That is, the integral J defined by the measure satisfies Equation (5.14) in Theorem 5.5.] Applications of this result to the construction of best invariant estimators are given.
Digital Object Identifier: 10.1214/cbms/1462061036