| Motivated by an application in computerized adaptive tests, we consider the following sequential design problem. There are J jobs to be processed according to a predetermined order. A single machine is available to process these J jobs. Each job under processing evolves stochastically as a Markov chain and earns rewards as it is processed, not otherwise. The Markov chain has transition probabilities parameterized by an unknown parameter. The objective is to determine how long each job should be processed so that the total expected rewards over an extended time interval is maximized. We construct a class of efficient strategies based on the theory of sequential testing. The example from computerized adaptive tests will be discussed and Analyzed using the method described in this talk. This is a joint work with C. D. Fuh of Academia Sinica. |