An extension of bayesian measure of information to regression
This paper extends Lindley's measure of average information to the linear model, E(Y∣s) = Xs. An expression which quantifies the average amount of information provided by the nxl vector of observations Y about the pxl vector of coefficient parameters s will be derived. The effect of the structure of the regressor matrix, X, on the information measure is discussed. An information theoretic optimal design is characterized. Some applications are suggested.