|Authors:||Jingjing Yang, Peng Ren|
|Title:||BFDA: A MATLAB Toolbox for Bayesian Functional Data Analysis|
|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.|
Page views:: 2986. Submitted: 2016-04-16. Published: 2019-05-09.
BFDA: A MATLAB Toolbox for Bayesian Functional Data Analysis
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