A Bayesian sequential procedure for determining the optimal number of interrogatory examples for concept-learning

The purpose of this paper is to derive optimal rules for sequential decision-making in intelligent tutoring systems. In a sequential mastery test, the decision is to classify a student as a master, a nonmaster, or to continue testing and administering another item. The framework of Bayesian sequential decision theory is used; that is, optimal rules are obtained by minimizing the posterior expected losses associated with all possible decision rules at each stage of testing and using techniques of backward induction. The main advantage of this approach is that costs of testing can be taken explicitly into account. The sequential testing procedure is demonstrated for determining the optimal number of interrogatory examples for concept-learning in the Minnesota adaptive instructional system. The paper concludes with an empirical example in which, for given maximum number of interrogatory examples for concept-learning in medicine, the appropriate action is indicated at each stage of testing for different number-correct score.