Adaptive Methodology for Functional Biomedical Data

描述（由申请人提供）：越来越多的生物医学研究产生精细网格采样的功能数据。这些类型的数据通常是高维且复杂的，具有许多不规则的特征，如峰值和变化点。目前缺乏现有的严格的统计方法来分析这类数据。本研究计划的目标是开发新的贝叶斯方法，为曲线样本的建模和执行推理提供统一的框架，该框架具有足够的灵活性，可以应用于各种应用，来自各种实验设计，并可以回答广泛的研究问题。1. 我们将在基于小波的功能混合模型框架内开发新的方法，该框架可容纳离群曲线，更广泛的曲线内协方差结构和高维功能数据，使其适用于广泛的功能数据。2. 我们将开发基于个体功能数据（如蛋白质组谱）对其进行分类的方法，这种方法允许我们将多个来源的功能和标量因子的信息结合起来。我们将开发执行贝叶斯功能假设检验的方法。3. 我们将开发自适应方法，将功能预测因子与功能反应联系起来。4. 我们将开发自适应功能主成分分析和基于主成分的功能混合模型的方法，这代表了一个数据驱动的建模框架，在考虑到功能数据中可能存在的复杂结构时非常灵活。5. 我们将把这些方法应用于一些与癌症相关的研究，产生功能数据，包括各种类型的蛋白质组学和基因组学数据。6. 我们将开发高效、易于使用、免费可用的代码，以适应本提案中描述的方法。

DESCRIPTION (provided by applicant): An ever-increasing number of biomedical studies yield functional data sampled on a fine grid. These type of data are frequently high dimensional and complex with many irregular features like peaks and change points. There is currently a dearth of existing rigorous statistical methods for analyzing this type of data. The goal of this research program is to develop new Bayesian methodology that provides a unified framework for modeling and performing inference on samples of curves that is flexible enough to apply to a variety of applications, from various experimental designs, and can answer a broad range of research questions. 1. We will develop new methodology within the wavelet-based functional mixed model framework that accommodates outlying curves, a broader class of within- curve covariance structures, and higher dimensional functional data, making it applicable to a broad range of functional data. 2. We will develop methods to classify individuals based on their functional data, e.g. proteomic profiles, in a way that allows us to combine information across functional and scalar factors of multiple sources. We will develop methods to perform Bayesian functional hypothesis testing. 3. We will develop adaptive methods for relating functional predictors to functional responses. 4. We will develop methods for adaptive functional principal components analysis and for principal component-based functional mixed models, which represents a data-driven modeling framework that is extremely flexible in taking into account the complex structure that may be present in the functional data. 5. We will apply the methods to a number of cancer-related studies yielding functional data, including various types of proteomics and genomics data. 6. We will develop efficient, easy-to-use, freely available code to fit the methods described in this proposal.