@article{JSSv089i02, title={BFDA: A MATLAB Toolbox for Bayesian Functional Data Analysis}, volume={89}, url={https://www.jstatsoft.org/index.php/jss/article/view/v089i02}, doi={10.18637/jss.v089.i02}, abstract={We provide a MATLAB toolbox, BFDA, that implements a Bayesian hierarchical model to smooth multiple functional data samples 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 samples to increase the smoothing accuracy, as well as simultaneously estimate the mean-covariance functions. 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 samples 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.}, number={2}, journal={Journal of Statistical Software}, author={Yang, Jingjing and Ren, Peng}, year={2019}, pages={1–21} }