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.
This research will develop flexible new quantitative methods that can be used to answer a wide range of research questions from complex functional data, which are increasingly encountered in biomedical research as a result of the technological innovations yielding automatic and high dimensional biological measurements. Our approach is to avoid making restrictive simplifying assumptions that do not fit the data, but instead to develop flexible methods that can adapt to their complex features, and thus extract rich information they contain regarding their underlying biological processes.
|Zhu, Hongxiao; Morris, Jeffrey S; Wei, Fengrong et al. (2017) Multivariate functional response regression, with application to fluorescence spectroscopy in a cervical pre-cancer study. Comput Stat Data Anal 111:88-101|
|Morris, Jeffrey S (2017) Comparison and Contrast of Two General Functional Regression Modeling Frameworks. Stat Modelling 17:59-85|
|Lee, Wonyul; Morris, Jeffrey S (2016) Identification of differentially methylated loci using wavelet-based functional mixed models. Bioinformatics 32:664-72|
|Morris, Jeffrey S; Gutstein, Howard B (2016) Detection and Quantification of Protein Spots by Pinnacle. Methods Mol Biol 1384:185-201|
|Zhang, Lin; Baladandayuthapani, Veerabhadran; Zhu, Hongxiao et al. (2016) Functional CAR models for large spatially correlated functional datasets. J Am Stat Assoc 111:772-786|
|Meyer, Mark J; Coull, Brent A; Versace, Francesco et al. (2015) Bayesian function-on-function regression for multilevel functional data. Biometrics 71:563-74|
|Lancia, Leonardo; Rausch, Philip; Morris, Jeffrey S (2015) Automatic quantitative analysis of ultrasound tongue contours via wavelet-based functional mixed models. J Acoust Soc Am 137:EL178-83|
|Fazio, Massimo A; Grytz, Rafael; Morris, Jeffrey S et al. (2014) Age-related changes in human peripapillary scleral strain. Biomech Model Mechanobiol 13:551-63|
|Fazio, Massimo A; Grytz, Rafael; Morris, Jeffrey S et al. (2014) Human scleral structural stiffness increases more rapidly with age in donors of African descent compared to donors of European descent. Invest Ophthalmol Vis Sci 55:7189-98|
|Wang, Wenting; Baladandayuthapani, Veerabhadran; Morris, Jeffrey S et al. (2013) iBAG: integrative Bayesian analysis of high-dimensional multiplatform genomics data. Bioinformatics 29:149-59|
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