Models for Choosing the Best Population

该奖项将通过调查统计规则来确定解决问题的一套给定方法中哪种方法是最佳的，从而为促进国家繁荣和经济福利做出贡献。这些规则将支持在更短的时间内做出更可靠的决定。在统计学的背景下，该项目将研究寻找确定n个人口中哪个人口的平均值最大的良好规则的方法。在每个阶段做出决定，决定下一个样本来自哪个总体，该决定是根据最终要求停止并宣布哪个总体具有最大平均值的规则来做出的。该项目将影响许多不同的应用领域，包括适应性临床试验、改进的随机优化程序以及各种在线广告活动的影响。该奖项将支持研究生，结果将通过包括教科书在内的各种渠道传播。该项目将研究人口分布为伯努利分布和正态分布时的模型，假设在这两种情况下，未知平均值都可以被视为具有已知分布的独立随机变量的值。考虑了不同的目标，例如在相对较少的预期观测值中选择平均值最大的总体，但条件是作出正确选择的概率至少是某个规定值；以及在观测值固定的情况下，找到具有很高的正确概率的最佳总体。该项目还考虑了当均值集合已知时的问题，但不知道哪个均值对应于哪个总体。讨论了这一主题的几个变种，包括一个模型，其中种群数量是无限的，目标是找到一个平均值至少是某个规定值的模型。还研究了一种模型，其中存在一组固定的项目，每个项目具有未知值，目标是通过随机比较找到具有最大值的项目。在每个阶段，直到停下来，个体都会看到决策者选择的项目的集合；决策者会了解个人更喜欢这些项目中的哪一个。假设某一项目与其价值成比例，感兴趣的问题是确定一种策略，该策略在经过相对较小的平均比较次数后，有很高的概率选择具有最高价值的项目。为了实现其目标，这项研究将结合和开发随机动态规划、模拟和随机模型分析方面的新技术。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This award will contribute to the advancement of national prosperity and economic welfare by investigating statistical rules for determining which of a given set of approaches to solving a problem is best. These rules will support the ability to make more reliable decisions in reduced time. In a statistical context, the project will study methods to find good rules for determining which of n populations has the largest mean. A decision is made at each stage as to which population to next sample from, with the decision made according to a rule which eventually calls for stopping and declaring which population has the largest mean. The project will impact many diverse application domains, including adaptive clinical trials, improved stochastic optimization procedures, and the impact of various online advertising campaigns. The award will support graduate students, and results will be disseminated through a variety of outlets, including textbooks.The project will study models both when the population distributions are Bernoulli and when they are normal, assuming in both cases that the unknown means can be regarded as being the values of independent random variables with known distributions. Different objectives are considered, such as choosing the population with the largest mean in a relatively small expected number of observations subject to the condition that the probability that a correct choice is made is at least some prescribed value; and of finding, with a high probability of being correct, the best population when the number of observations is fixed. The project also considers the problem when the set of means is known, but it is unknown which mean corresponds to which population. Several variations on this theme are addressed, including a model where the number of populations is unlimited and the objective is to find one whose mean is at least some prescribed value. Also studied is a model where there are a fixed set of items, each having an unknown value, and the objective is to find, via random comparisons, the item having the largest value. At every stage until stopping, an individual is shown a collection of items of the decision-maker's choice; the decision-maker learns which of these items the individual prefers. Assuming that an item is preferred in proportion to its value, the problem of interest is to determine a policy that has a high probability of choosing the item with the highest value after a relatively small mean number of comparisons. To obtain its goals, the research will combine and develop new techniques in stochastic dynamic programming, simulation, and stochastic model analysis.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.