Adaptive Designs

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。 研究人员将开发随着时间的推移适应传入数据的统计实验设计-所谓的“自适应设计”-并计划分析两类问题的此类实验的数据：（I）最佳参数估计，控制和非线性模型多期回归问题的设计（例如，广义线性模型），和（II）多个假设的时序检验。在第一部分中，最近的计算进展，称为近似动态规划将被利用，为发展非线性回归模型的最佳或接近最佳的估计和控制程序的承诺。在第二部分中，将使用和扩展最新的方法学进展，以制定一种统一的方法来测试多个假设随着时间的推移或在统计上最佳的方式，无论是强（FWER）或弱（FDR）的错误控制阶段。 对于这两个部分，所产生的程序的性能将进行分析研究，通过广泛的数值模拟评估，并适用于真实的数据。 在经济学，DNA微阵列数据，心理测试，生物医学试验和工程控制问题的应用将得到解决，和实用的算法将开发真实的，在这些领域的在线实施。许多具有重大社会意义的统计挑战需要适应一个人的行动迅速和智能的新信息随着时间的推移到达。 其中一些领域包括太阳能、机器人、汽车排放、国土安全和医疗保健。在这个项目中，研究人员将开发统计程序和算法，这些程序和算法是这些领域中一些最具挑战性的问题的基础。该项目的第一部分涉及回归问题，其中观察者可以影响生成统计信息的设置，以及如何随着时间的推移设计和更改这些设置，以便最有效地了解未知参数并控制所选设置的效果。 最近的计算进步被称为近似动态规划，有可能解决以前这种形式的棘手问题。 第二部分涉及如何最有效地将来自不同来源的统计信息联合收割机组合起来，以得出合理的结论，以及如何避免错误发现的多重检验谬误。 这些问题的理论基础将进行研究，以开发数据分析和计算算法，用于真实的，在线实施，并将开发软件包，以促进应用。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). The investigator will develop designs for statistical experiments that adapt over time to incoming data -- so-called "adaptive designs" -- and plans for analyzing data coming out of such experiments for two general classes of problems: (I) optimal parameter estimation, control, and design in multiperiod regression problems with nonlinear models (e.g., generalized linear models), and (II) time-sequential tests of multiple hypotheses. In Part I, recent computational advances known as approximate dynamic programming will be harnessed that hold promise for developing optimal or nearly-optimal estimation and control procedures in nonlinear regression models. In Part II, recent methodological advances will be used and extended to develop a unified approach to testing multiple hypotheses over time or in stages in a statistically optimal way, with either strong (FWER) or weak (FDR) error control. For both parts, the performance of the resulting procedures will be studied analytically, assessed through extensive numerical simulations, and applied to real data. Applications in economics, DNA microarray data, psychometric testing, biomedical trials, and engineering control problems will be addressed, and practical algorithms will be developed for real, on-line implementation in these areas.Many statistical challenges of great societal importance require adapting one's actions quickly and intelligently as new information arrives over time. Some of these areas include solar energy, robotics, automobile emissions, homeland security, and health care. In this project the investigator will develop the statistical procedures and algorithms that underlie some of the most challenging problems in these areas. Part I of this project concerns regression problems, where the observer can influence the settings under which statistical information is generated, and how to design and change these settings over time in order to most efficiently learn about unknown parameters and control the effects of the chosen settings. Recent computational advances known as approximate dynamic programming hold the potential to solve previously intractable problems of this form. Part II concerns how to most efficiently combine statistical information from many disparate sources over time in order to reach justified conclusions, and how to avoid the multiple testing fallacy of false discoveries. The theory underlying these problems will be studied to develop data analysis and computational algorithms for real, on-line implementation, and software packages will be developed to facilitate applications.