A Bayesian approach for simultaneous optimization of test-based decisions is presented using the example of a selection decision for a treatment followed by a mastery decision. A distinction is made between weak and strong rules, and conditions for monotonicity of optimal weak and strong rules are presented. (Author/SLD)

This paper presents some Bayesian theories of simultaneous optimization of decision rules for test-based decisions. Simultaneous decision making arises when an institution has to make a series of selection, placement, or mastery decisions with respect to subjects from a population. An obvious example is the use of individualized instruction in…

A method is proposed for optimizing cutting scores for a selection-placement-mastery problem simultaneously. A simultaneous approach has two advantages over separate optimization. First, test scores used in previous decisions can be used as "prior data" in later decisions, increasing the efficiency of the decisions. Then, more realistic…

The purpose of this paper is to simultaneously optimize decision rules for combinations of elementary decisions. As a result of this approach, rules are found that make more efficient use of the data than does optimizing those decisions separately. The framework for the approach is derived from empirical Bayesian theory. To illustrate the…