Variational Bayesian functional PCA

A Bayesian approach to analyze the modes of variation in a set of curves is suggested. It is based on a generative model thus allowing for noisy and sparse observations of curves. A Demmler–Reinsch(-type) basis is used to enforce smoothness of the latent (‘eigen’)functions. Inference, including estimation, error assessment and model choice, particularly the choice of the number of eigenfunctions and their degree of smoothness, is derived from a variational approximation of the posterior distribution. The proposed analysis is illustrated with simulated and real data.