Ranking and Selection
Ranking and Selection
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DOI：
10.1145/3241042
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发表时间：
2014-10
期刊：
影响因子：
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通讯作者：
Björn Görder;M. Kolonko
中科院分区：
文献类型：
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作者：
Björn Görder;M. Kolonko
我们引入了一个新的抽样方案，选择最好的替代品的一组给定的系统进行评估，相对于他们的预期性能。我们假设系统是在计算机上模拟的，并且所有系统的联合观测具有未知均值和协方差矩阵的多元正态分布。特别地，系统的观测可以是随机相关的，就像使用公共随机数进行模拟的情况一样。在算法的每次迭代中，我们为替代方案分配固定的模拟运行预算。我们使用贝叶斯设置与noninformative先验分布，并推导出一个新的封闭形式的近似的后验分布，允许提供一个正确的选择（PCS）的后验概率的下限。继续迭代直到对于给定的α，这个下限大于1−α。我们还介绍了一种新的分配策略，分配可用的预算根据后验误差概率。我们的程序不需要额外的先验参数，可以科普不同类型的排名和选择任务。我们的数值实验表明，我们的策略是上级从文献中的其他程序，即KN++和Pluck。在我们的所有测试场景中，这些程序需要更多的观察和/或具有低于所需1−α的经验PCS。我们的过程总是有其经验PCS高于1−α，强调了我们的后验分布近似的实用性。
We introduce a new sampling scheme for selecting the best alternative out of a given set of systems that are evaluated with respect to their expected performances. We assume that the systems are simulated on a computer and that a joint observation of all systems has a multivariate normal distribution with unknown mean and unknown covariance matrix. In particular, the observations of the systems may be stochastically dependent as is the case if common random numbers are used for simulation. In each iteration of the algorithm, we allocate a fixed budget of simulation runs to the alternatives. We use a Bayesian set-up with a noninformative prior distribution and derive a new closed-form approximation for the posterior distributions that allows provision of a lower bound for the posterior probability of a correct selection (PCS). Iterations are continued until this lower bound is greater than 1−α for a given α. We also introduce a new allocation strategy that allocates the available budget according to posterior error probabilities. Our procedure needs no additional prior parameters and can cope with different types of ranking and selection tasks. Our numerical experiments show that our strategy is superior to other procedures from the literature, namely, KN++ and Pluck. In all of our test scenarios, these procedures needed more observation and/or had an empirical PCS below the required 1−α. Our procedure always had its empirical PCS above 1−α, underlining the practicability of our approximation of the posterior distribution.