Title: Bayesian function-on-function regression for multilevel functional data.

Authors: Meyer, Mark J; Coull, Brent A; Versace, Francesco; Cinciripini, Paul; Morris, Jeffrey S

Published In Biometrics, (2015 Sep)

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.

PubMed ID: 25787146

MeSH Terms: Algorithms; Bayes Theorem*; Brain Mapping/methods*; Brain/physiology*; Computer Simulation; Data Interpretation, Statistical; Evoked Potentials/physiology*; Humans; Models, Statistical*; Regression Analysis*; Wavelet Analysis