Some applications of Bayesian decision theory to intelligent tutoring systems are considered. How the problem of adapting the appropriate amount of instruction to the changing nature of a student's capabilities during the learning process can be situated in the general framework of Bayesian decision theory is discussed in the context of the Minnesota Adaptive Instructional System (MAIS). Two basic elements of this approach are used to improve instructional decision making in intelligent tutoring systems. First, it is argued that in many decision-making situations the linear loss model is a realistic representation of the losses actually incurred. Second, it is shown that the psychometric model relating observed test scores to the true level of functioning can be represented by Kelley's regression line from classical test theory. Optimal decision rules for the MAIS are derived using these two features. (Contains 3 tables, 1 figure, and 42 references.) (SLD)