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1991 subject classification adaptive biased coin adaptive designs Adaptive Designs IMS allocation rule allocation scheme American Statistical Association AMS 1991 subject approximation assume asymptotic asymptotically optimal backward induction bandit problem Bayesian Behrens-Fisher problem biased coin design binomial set Biometrika central limit theorem clinical trials computational defined denote Designs IMS Lecture dose levels Durham dynamic programming Eisele estimation ethical evaluate example expected number extreme value failure Flournoy Gittins Gittins index given Hardwick IMS Lecture Notes inferior treatments Markov martingale minimize Monograph Series 1995 normal number of patients observations obtained optimal design P(CS parameters percentile play-the-winner posterior prior distribution quantile random variables random walk renewal theory response function RHLB Robbins sample Section selection bias sequence sequential designs sequential procedure stage stationary treatment distribution stopping rule stress level target Theorem tion total number treatment allocation unknown up-and-down designs variance
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Page 217 - Thus A - Et is the ordinary i-th component of A. More generally, if B is a unit vector, not necessarily one of the Eh then we have simply c = AB because B - B = 1 by definition of a unit vector. Example 6. Let A = (1, 2, -3) and B = (1, 1, 2). Then the component...
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Page 139 - F < 1. We further assume that it is desirable to 'center' the distribution of treatments around the unknown quantile. This is accomplished by sequentially assigning treatment levels to subjects using upand-down rules, that is, rules by which the treatment used in the next trial is restricted to be one level higher, one level lower, or the same as it is for the current trial. We describe two such rules that asymptotically result in a unimodal distribution of treatment assignments with mode as close...