Abstract: We show how to compute optimal designs and exact analyses of allocation rules for various response-adaptive sampling problems. The problems we have solved include parameter estimation in an industrial scenario, and testing in a clinical trial, and subsequent to this paper we have solved many more (see the Related Work below). The adaptive sampling procedures are designed using a Bayesian approach, but they, and any other procedure, can be exactly analyzed along Bayesian or frequentist criteria. Our computational approach incorporates dynamic programming (also known as backward induction) and a new technique of path induction. By utilizing efficient algorithms and careful implementation, we are able to determine exact solutions to practical problems previously approached only through simulation or approximation.
Keywords: constrained dynamic programming, path induction, response adaptive sampling procedure, design of experiments, sequential allocation, backward induction, bayesian design, multiple objective criteria, controlled clinical trial, adaptive allocation, stochastic optimization, computational learning theory, bandit problem
Complete paper. This paper appears in Adaptive Designs, N. Flournoy and W.F. Rosenberger, eds., IMS Lecture Notes--Monograph Series 25, 1995, pp. 223-237.
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