Bayesian function‐on‐function regression for multilevel functional data

Mark J. Meyer, Brent A. Coull, Francesco Versace, Paul Cinciripini and Jeffrey S. Morris

Biometrics, 2015, vol. 71, issue 3, 563-574

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.

Date: 2015
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