title: Bayesian function-on-function regression for multilevel functional data.
abstract: Medical and public health research increasingly involves the collection of complex and high dimensional data. In particular, functional data-where the unit of observation is a curve or set of curves that are finely sampled over a grid-is frequently obtained. Moreover, researchers often sample multiple curves per person resulting in repeated functional measures. A common question is how to analyze the relationship between two functional variables. We propose a general function-on-function regression model for repeatedly sampled functional data on a fine grid, presenting a simple model as well as a more extensive mixed model framework, and introducing various functional Bayesian inferential procedures that account for multiple testing. We examine these models via simulation and a data analysis with data from a study that used event-related potentials to examine how the brain processes various types of images.
authors: Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania, U.S.A.
authors: Mark J
authors: MJ
authors: Meyer
authors: Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, Massachusetts, U.S.A.
authors: Brent A
authors: BA
authors: Coull
authors: The University of Texas M.D. Anderson Cancer Center, Houston, Texas, U.S.A.
authors: Francesco
authors: F
authors: Versace
authors: The University of Texas M.D. Anderson Cancer Center, Houston, Texas, U.S.A.
authors: Paul
authors: P
authors: Cinciripini
authors: The University of Texas M.D. Anderson Cancer Center, Houston, Texas, U.S.A.
authors: Jeffrey S
authors: JS
authors: Morris
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D001921:Brain / Q000502:physiology*; D001931:Brain Mapping / Q000379:methods*; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D005071:Evoked Potentials / Q000502:physiology*; D006801:Humans; D015233:Models, Statistical; D012044:Regression Analysis; D058067:Wavelet Analysis
keywords: Basis functions; Bayesian inference; Function-on-function regression; Functional data analysis; Functional mixed models; Functional testing; Principal components; Wavelet regression