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  1. (, Operations research letters)
    We develop recursions for computing the mean and variance of the number of pooled tests needed by the halving scheme to determine the disease positive members of a population. It is assumed that each population member is independently positive with probability p, that the individual blood samples can be pooled to test whether or not at least one member of that pooled group is positive, and that a positive tested group is then split in half and the process continued. 
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  2. ; (, Journal of Applied Probability)
    Abstract We consider the Bernoulli bandit problem where one of the arms has win probability α and the others β, with the identity of the α arm specified by initial probabilities. With u = max(α, β), v = min(α, β), call an arm with win probability u a good arm. Whereas it is known that the strategy of always playing the arm with the largest probability of being a good arm maximizes the expected number of wins in the first n games for all n , we conjecture that it also stochastically maximizes the number of wins. That is, we conjecture that this strategy maximizes the probability of at least k wins in the first n games for all k , n . The conjecture is proven when k = 1, and k = n , and when there are only two arms and k = n - 1. 
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