The Value of Information for Correlated GLMs

We examine the situation where a decision maker is considering investing in a number of projects with uncertain revenues. Before making a decision, the investor has the option to purchase data which carry information about the outcomes from pertinent projects. When these projects are correlated, the data are informative about all the projects. The value of information is the maximum amount the investor would pay to acquire these data. In this paper we discuss the case where the outcome of each project is modelled by an exponential family. When the distribution is non-Gaussian, the value of information does not have a closed form expression. We use the Laplace approximation and matrix approximations to derive an analytical expression to the value of information, and examine its sensitivity under different parameter settings and distributions. In the Gaussian case the proposed technique is exact. Our analytical method is compared against the alternative MonteCarlo method, and we show similarity of results for various sample sizes of the data. The closed form results are much faster to compute. Application of the method is presented in a spatial decision problem for treating the Bovine Tuberculosis in the United Kingdom, and for rock fall avoidance decisions in a Norwegian mine.