Comment on “Conditional Simulation and the Value of Information: A Bayesian Approach” by A.R. Solow and S.J. Ratick

Abstract

Solow and Ratick present an example of the use of conditional simulation for determining whether additional sample information is valuable. When used for this type of risk analysis, geostatistical conditional simulation is simply an adaptation of classical Monte Carlo methods to a spatial setting. There is an implicit assumption with such methods that the outcomes used in the calculations are equiprobable. For example, Solow and Ratick’s equation for approximating the expected net benefit is an equally-weighted average of the net benefit calculated on Kindependent realizations:

$$E\left( {E*\left( Z \right)|x} \right) = \frac{1}{K}\sum\limits_{{j = 1}}^{K} {E*\left( {z_{{|x}}^{j}} \right)}$$

. Such a calculation is perfectly reasonable if any one of the Krealizations is as likely as any other one. If the realizations are not equiprobable—if the computer code that generates them is not fairly sampling the full space of uncertainty—then the whole approach is compromised. A non-representative set of outcomes will lead to a biased calculation and, possibly, to erroneous decisions.