Sequential Decision Making

The purpose of this entry is to describe optimal rules for sequential mastery tests in the context of education. In a sequential mastery test, the decision is to classify a student as a master, a nonmaster, or to continue testing and administering another random 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. The main advantage of this approach is that costs of testing can be taken explicitly into account. For given maximum number of items to be administered, it is shown how the appropriate action can be computed at each stage of testing for different number-correct score. Keywords: sequential mastery testing; Bayesian sequential rules; backward induction; binomial distribution; threshold loss