Combining site‐specific and regional information: An empirical Bayes Approach

Abstract

Empirical Bayes theory, adapted to a hydrologic context, is used to develop procedures for inferring hydrologic quantities by combining site‐specific and regional information. It ‘borrows strength’ from ‘similar’ basins to improve upon inference at a particular basin. The superpopulation is a key concept in the empirical Bayes approach. It is a probability distribution from which basin parameters are randomly assigned, a conceptualization closely related to regionalization models. It is inferred from observable regional data and expresses the degree of basin ‘similarity’ in a region. This approach treats regionalized estimators as a special case and leads to procedures similar to James‐Stein estimators. Empirical Bayes procedures can lead to substantial improvements in performance over site‐specific procedures. However, for basins which are very different from the majority, site‐specific procedures may perform better. The method of moments approach to inferring the superpopulation is considered in detail. Finally, two examples in flood frequency analysis are presented to illustrate various facets of empirical Bayes procedures.