Multimodel ranking and inference in ground water modeling.

Uncertainty of hydrogeologic conditions makes it important to consider alternative plausible models in an effort to evaluate the character of a ground water system, maintain parsimony, and make predictions with reasonable definition of their uncertainty. When multiple models are considered, data collection and analysis focus on evaluation of which model(s) is(are) most supported by the data. Generally, more than one model provides a similar acceptable fit to the observations; thus, inference should be made from multiple models. Kullback-Leibler (K-L) information provides a rigorous foundation for model inference that is simple to compute, is easy to interpret, selects parsimonious models, and provides a more realistic measure of precision than evaluation of any one model or evaluation based on other commonly referenced model selection criteria. These alternative criteria strive to identify the true (or quasi-true) model, assume it is represented by one of the models in the set, and given their preference for parsimony regardless of the available number of observations the selected model may be underfit. This is in sharp contrast to the K-L information approach, where models are considered to be approximations to reality, and it is expected that more details of the system will be revealed when more data are available. We provide a simple, computer-generated example to illustrate the procedure for multimodel inference based on K-L information and present arguments, based on statistical underpinnings that have been overlooked with time, that its theoretical basis renders it preferable to other approaches.