  We provide a MATLAB toolbox, BFDA, that implements a Bayesian hierarchical
model to smooth multiple functional data with the assumptions of the same
underlying Gaussian process distribution, a Gaussian process prior for the mean
function, and an Inverse-Wishart process prior for the covariance function.
This model-based approach can borrow strength from all functional data to
increase the smoothing accuracy, as well as estimate the mean-covariance
functions simultaneously. An option of approximating the Bayesian inference
process using cubic B-spline basis functions is integrated in BFDA, which
allows for efficiently dealing with high-dimensional functional data. Examples
of using BFDA in various scenarios and conducting follow-up functional
regression are provided. The advantages of BFDA include: (1) Simultaneously
smooths multiple functional data and estimates the mean-covariance functions in
a nonparametric way; (2) flexibly deals with sparse and high-dimensional
functional data with stationary and nonstationary covariance functions, and
without the requirement of common observation grids; (3) provides accurately
smoothed functional data for follow-up analysis.
