A Bayesian regression model for multivariate functional data

In this paper we present a model for the analysis of multivariate functional data with unequally spaced observation times that may differ among subjects. Our method is formulated as a Bayesian mixed-effects model in which the fixed part corresponds to the mean functions, and the random part corresponds to individual deviations from these mean functions. Covariates can be incorporated into both the fixed and the random effects. The random error term of the model is assumed to follow a multivariate Ornstein-Uhlenbeck process. For each of the response variables, both the mean and the subject-specific deviations are estimated via low-rank cubic splines using radial basis functions. Inference is performed via Markov chain Monte Carlo methods.