In an invitational address to the Victorian Institute of Educational Research, the author discussed Bayesian theory and its relationship to the design and construction of tailored or adaptive tests. Bayesian thinking involves recognizing the role of prior probabilities and using these probabilities in combination with new data to arrive at future…

Educational assessment concerns inference about student knowledge, skills, and accomplishments. Test theory has evolved in part to address questions of weight, coverage, and import of data. Resulting concepts and techniques can be viewed as applications of more general principles for inference in the presence of uncertainty. (SLD)

A general approach is proposed for modeling the structure of a two-way contingency table, and for drawing inferences about the marginal and interaction effects, cell parameters, and conditional probabilities. The prior distribution expresses uncertainty in a simple reduced model, in particular the independence model. The posterior estimates of the…