A decision theory approach is used to model the information retrieval decision problem of which documents to retrieve from a library collection in response to a specific user query for information. A thorough discussion of decision theory, including the components of the alternatives, states-of-nature, outcomes, and evaluations-as well as of the optimization process under the cases of certainty, risk, and uncertainty-is presented. Bayesian statistics are also discussed to show how prior information about the various documents via classification analysis can affect the decision process under risk. An example problem is used to illustrate the decision theory approach and to compare the overall performance of the retrieval system under risk with and without the document classification information. Thus, the operations research technique of decision theory is used to model the retrieval decision process, illustrate how important evaluation is, and to demonstrate the value of prior information via document classification analysis. Moreover, the paper presents, in a somewhat tutorial mode, an overall framework for considering the information retrieval decision problem, incorporating the aspects of cost-effectiveness and alternative evaluation, which allows one to better understand the contributions made by many researchers in this crucial area. [ABSTRACT FROM AUTHOR]