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.
Meyer, Mark J.; Coull, Brent A.; Versace, Francesco; Cinciripini, Paul; and Morris, Jeffrey S.. "Bayesian Function-on-Function Regression for Multilevel Functional Data." Biometrics 71, no. 3 (2015) : 563-574.