Function-on-Function Mixed Models via Bayesian Wavelet Regression, a Lecture by Mark Meyer (Updated 9/19/13)
Medical and public health research increasingly involves the collection of more and more 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. Both one and two sample settings are presented along with a Bayesian inference procedure. We will examine these models via simulation and a data analysis. Motivating data come from a neurological study examining how the brain processes various types of images. Subjects were taken from a pre-screening for a smoking cessation trial. Event-related potentials were then measured after presentation of neutral, positive, negative, and cigarette-related images. Our analysis will focus on the relationship between measurements from pairs of sensors during neutral and cigarette-related image presentation. Lecture by Dr. Mark Meyer, Harvard University.