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组方法中哪一种是最好的，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策的能力。 在统计学方面，该项目将研究方法，以找到确定n个总体中哪一个具有最大平均值的良好规则。在每个阶段都要决定下一个样本来自哪个总体，并根据最终要求停止并宣布哪个总体具有最大均值的规则做出决定。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，并将通过各种渠道，包括教科书，传播成果。该项目将研究模型时，人口分布是伯努利和当他们是正常的，假设在这两种情况下，未知的平均值可以被视为具有已知分布的独立随机变量的值。 不同的目标被认为是，如选择人口与最大的平均值在一个相对较小的预期数量的观察受的条件下，一个正确的选择的概率是至少一些规定的值;和发现，具有很高的概率是正确的，最好的人口时，观察的数量是固定的。该项目还考虑了当均值集已知，但不知道哪个均值对应于哪个总体时的问题。 这一主题的几个变化，包括一个模型的人口数量是无限的，目标是找到一个其平均值至少是一些规定的值。 还研究了一个模型，其中有一组固定的项目，每个项目都有一个未知的值，目标是通过随机比较，找到具有最大值的项目。 在每个阶段，直到停止，一个人被展示了决策者的选择项目的集合;决策者学习这些项目中的个人更喜欢。 假设一个项目的优先级与其价值成比例，感兴趣的问题是确定一个策略，该策略在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，该研究将联合收割机和开发随机动态规划，模拟和随机模型分析的新技术。该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.