Numerical Techniques for Evaluating Sample Information

Abstract

This paper is concerned with the evaluation of multiple integrals to determine the Expected Value of Sample Information (EVSI). It first examines the accuracy and the computational efficiency of the existing numerical methods—the numerical integration method, the Monte Carlo method, and the fixed fractile method—as applied to double integrals. It then develops two new methods—the numerical integration method and the quadrature method. These methods are applicable, not only to double integrals, but also to integrals of higher dimensions. The proposed numerical integration method is made possible by deriving an alternate expression for EVSI. This method yields accurate results, which allows us to ascertain the accuracy of other methods. The quadrature method has greatly increased the computational efficiency over the methods presently available. This efficiency makes it feasible to find optimal sample sizes for problems in multivariate statistical analysis.