Smoothing Functional Data with Bayesian Method

We will develop a Bayesian method for smoothing raw functional data. Functional data are generally obtained from discrete noisy observations of continuous curves. Typically, smoothing each curve is treated as a single nonparametric regression problem. We investigate a robust method that borrows strength from all of the measured curves, i.e. across all realizations of the functions. Simulations and application to real case studies will be presented. This novel nonparametric model could be used widely in many application areas, such as smoothing spectrum data, as they are all continuous data curves and could be treated as a function of some variables.