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.