Parameter Estimation in Water Resources Planning and Management: Optimal Actions or Optimal Parameters?

The optimality of parameter estimates is commonly justified on the basis of their sampling properties in parameter space (e.g., minimum mean square error, unbiasedness). However, these criteria may not be necessarily appropriate within the small sample size environment and the management rather than inferential focus of water resource planning decisions. Using two general cases, it is shown that in the presence of parameter uncertainty, “optimal” parameters, selected on the basis of their sampling properties in parameter space, can instead lead to nonoptimal decisions relative to planning objectives. In either case, alternative (informative and noninformative) Bayesian estimators are presented which, by incorporating parameter uncertainty, lead to uniform improvements in efficiency in action space over the traditional estimators. Incorporation of parameter uncertainty will not necessarily lead to uniform improvements, however. A counterexample is presented which shows that the use of noninformative priors, while optimal in the first case, can instead result in uniformly poorer decisions relative to the traditional estimators in the second case. The potential inefficiencies due to the use of noninformative measures of uncertainty and/or the misspecification of the prior in Bayesian estimators, provide a motivation for the consideration instead of empirical Bayes methods of estimation.