Variational Bayes for Basis Selection in Functional Data Representation with Correlated Errors

Music City Center 

Functional data analysis (FDA) has found extensive application across various fields, driven by the increasing recording of data continuously over a time interval or at several discrete points. FDA provides the statistical tools specifically designed for handling such data. Over the past decade, Variational Bayes (VB) algorithms have gained popularity in FDA, primarily due to their speed advantages over MCMC methods. This work proposes a VB algorithm for basis function selection for functional data representation while allowing for a complex error covariance structure. We assess and compare the effectiveness of our proposed VB algorithm with MCMC via simulations. We also apply our approach to a publicly available dataset. Our results show the accuracy in coefficient estimation and the efficacy of our VB algorithm to find the true set of basis functions. Notably, our proposed VB algorithm demonstrates a performance comparable to MCMC but with substantially reduced computational cost.

Bayesian inference

Functional data

Variational EM

Basis function selection

Correlated errors 

Section on Bayesian Statistical Science