The primary objective of this proposal is to develop adaptive and exible statistical models for analyses of multivariate, functional and spatial data from high-throughput biomedical studies. These studies raise computational, modeling, and inferential challenges with respect to high-dimensionality as well as structured dependency induced by the various aspects of the processes generating the data. Our work is motivated by, and will be applied to, data from a variety of high- throughput cancer-related studies that were conducted by our biomedical collaborators, in genomics, epigenomics and transcriptomics;although our methods are generally applicable to other contexts. The short-term objective of this research is to develop novel statistical methods and computational tools for statistical and probabilistic modeling of such high-throughput data with particular emphasis on integrative methods to combine information within and across dierent assays as well as clinical data to answer important biological questions. Our long-term goal is to improve risk prediction and treatment selection in cancer prevention, diagnosis and prognosis. We will accomplish the objective of this application by pursuing the following ve specic aims (1) develop new methodology for Bayesian adaptive generalized functional linear mixed models, allowing for local and nonlinear association structures between scalar responses and functional predictors (2) develop hierarchical Bayesian joint models for integrating diverse types of multivariate and functional data. (3) develop Bayesian spatial-functional process models for spatially indexed high-dimensional functional data, methods for data requiring a broader class of within-function and between-function covariance structures using exible families of covariance functions. (4) develop multivariate Bayesian spatial-functional models for joint modeling of multiple spatially indexed functional data. (5) develop ecient, user-friendly and freely available software for the proposed methods.
This project will have significant impact on integrative analysis of various types of genetic data, as well as clinical data. This will results in a better understanding of the underlying biological mechanisms of cancer - leading to better prevention and treatment strategies and improve cancer patient care.
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