Collaborative Research: FRG: New development on nonparametric modeling and inferences with biological applications

本提案的目标是开发新的和广泛适用的半参数和非参数方法来解决计算生物学中具有挑战性的统计问题。生物研究的前沿，如微阵列和蛋白质组数据的规范化和分析，大脑的功能连接，纵向和功能数据的协变量效应，以及个体反应轨迹的预测，已经产生了许多突出的统计挑战。一些新的半参数和非参数模型已经被引入以满足上述生物应用的迫切需要。提出了一些关于非参数估计和推理的创新方法。它们的性质将通过渐近理论和模拟来研究。它们在生物应用方面的功效将被仔细审查。本文不仅介绍了一些创新的技术和有用的统计模型，而且对非参数推理提供了各种新的见解。研究结果将对统计理论和方法的未来发展产生重大影响。技术发明和信息的进步使科学研究和技术发展发生了革命性的变化。定量方法已广泛应用于科学界。他们在知识发现中发挥了关键作用。本提案旨在发展新的非参数技术和理论，这些技术和理论出现在科学发展的前沿。特别是，研究人员将为微阵列，蛋白质组学，纵向和功能数据以及fMRI脑图像的分析开发模型和尖端技术。这些数据的共同特征是它们的复杂性和规模，而非参数技术在这方面特别强大和不发达。提出的技术解决了分子生物学、神经病学和流行病学计算方面的迫切需求。此外，他们还将把新的数学发展与科学和工程领域的发展相结合，从而促进新知识的发现和审慎的决策。作为这项研究的结果，本科生和研究生、博士后和代表性不足的群体将得到培训。

The objectives of this proposal are to develop new and widely applicablesemiparametric and nonparametric approaches to solve challengingstatistical problems from computational biology. Frontiers of biologicalresearch such as normalization and analysis of microarray and proteomicdata, functional connectivity of brains, covariate effects on longitudinaland functional data, and prediction of individual response trajectorieshave generated a number of outstanding statistical challenges. Severalnew semiparametric and nonparametric models have been introduced toaddress the imminent needs for the aforementioned biological applications. A number of innovative methods on nonparametric estimation and inferencesare proposed. Their properties will be investigated via both asymptotictheory and simulations. Their efficacy in biological applications will becarefully scrutinized. This proposal not only introduces a number ofinnovative techniques and useful statistical models, but also providesvarious new insights into nonparametric inferences. The research findingswill have significant impact on the future development of statisticaltheories and methodologies.Technological invention and information advancement have revolutionizedscientific research and technological development. Quantitative methodshave been widely employed in scientific communities. They have playedpivotal roles in knowledge discovery. This proposal intends to developnew nonparametric techniques and theories that arise from frontiers ofscientific development. In particular, the investigators will developmodels and cutting-edge technologies for the analysis of microarray,proteomic, longitudinal and functional data and fMRI brain images. Commoncharacteristics of these data are their complexity and size, wherenonparametric techniques are particularly powerful and under developed.The proposed techniques address imminent needs in computational aspects ofmolecular biology, neurology, and epidemiology. In addition, they willintegrate new mathematical developments with those in science andengineering, which empowers new knowledge discoveries and prudent policymaking. Undergraduate and graduate students, postdoctors andunderrepresented groups will be trained as results of this research.