Proximal Decision Analysis with Imperfect Information

In proximal decision analysis the value of a decision depends on a vector of state variables s and a vector of decision variables d in a quadratic fashion. Suppose some data, represented by a vector x, can be obtained. This paper describes a technique for using the data and develops an expression for the value of the information conveyed by the data. Because the value model is quadratic the data processing procedure uses a linear minimum-variance estimate of the conditional mean of s which depends only on the prior moments of the state vector and the noise associated with the measurement.