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

这个建议的目标是开发新的和广泛适用的半参数和非参数的方法来解决挑战性的统计问题，从计算生物学。生物学研究的前沿领域，如微阵列和蛋白质组学数据的标准化和分析、大脑的功能连接、对大脑和功能数据的协变量效应以及个体反应概率的预测，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，以解决上述生物应用的迫切需要。 提出了一些非参数估计和推断的新方法。它们的性质将通过渐近理论和模拟来研究。 它们在生物学应用中的功效将受到仔细的审查。 这一建议不仅引入了一些创新的技术和有用的统计模型，而且还提供了各种新的见解非参数推断。 这些研究成果将对未来医学理论和方法的发展产生重大影响，技术发明和信息技术的进步使科学研究和技术发展发生了革命性的变化。定量方法在科学界得到了广泛的应用。 它们在知识发现中起着举足轻重的作用。 该建议旨在发展新的非参数技术和理论，这些技术和理论来自科学发展的前沿。特别是，研究人员将开发用于分析微阵列，蛋白质组学，纵向和功能数据以及fMRI脑图像的模型和尖端技术。这些数据的共同特点是它们的复杂性和规模，其中非参数技术特别强大，但尚未得到开发。所提出的技术解决了分子生物学、神经学和流行病学计算方面的迫切需要。此外，他们将把新的数学发展与科学和工程学的发展结合起来，这将促进新的知识发现和谨慎的决策。 本科生和研究生，博士后和代表性不足的群体将作为这项研究的结果进行培训。

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.