Exploring Imprecise Probability Assessments Based on Linear Constraints.
Radu Lazar, Glen D. Meeden · 2003
For many problems there is only sufficient prior information for a Bayesian decision maker to identify a class of possible prior distributions. In such cases it is of interest to find the range of possible values for the prior expectation for some real valued function of the parameter of interest. Here we show how this can be done when the imprecise prior assessment is based on linear constraints. In particular we find the joint range of possible values for a pair of such functions. We also study the joint range of the posterior expectation for a pair of functions.