EMPIRICAL BAYES ESTIMATION AND INFERENCE FOR THE PHOSPHORUS–CHLOROPHYLL RELATIONSHIP IN LAKES

ABSTRACT

State and regional agencies frequently must use a model or models to assess limnological relationships, like that between phosphorus and chlorophyll, in a large number of lakes. If lake behavior in all lakes is essentially identical, then it is reasonable to pool information across lakes concerning the relationships and to make inferences on the basis of a universal model. Alternatively, if all lakes are unique, then inferences must be drawn from lake-specific models. The truth probably lies somewhere in between these two extremes. On that basis, empirical Bayes estimation is used to fit a simple model relating phosphorus to chlorophyll in lakes. The model is then applied to each lake in such a way that the chlorophyll prediction is based on both lake-specific and regional lake information. For lakes as a whole, the empirical Bayes estimator should result in improved predictions over standard approaches.