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Fast Bayesian Functional Principal Components Analysis.

Joseph Sartini1, Xinkai Zhou1, Elizabeth Selvin2

  • 1Department of Biostatistics, Johns Hopkins University, Baltimore, MD.

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|April 8, 2026
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Summary
This summary is machine-generated.

We introduce FAST, a fully-Bayesian Functional Principal Components Analysis (FPCA) method. FAST improves stability and performance in dimension reduction for functional data by accounting for estimation uncertainty.

Keywords:
Bayesian methodsFunctional dataSemiparametric methodsUncertainty quantification

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Area of Science:

  • Statistics
  • Biostatistics
  • Data Science

Background:

  • Functional Principal Components Analysis (FPCA) is crucial for reducing the dimensionality of functional data.
  • Traditional FPCA methods treat estimated principal components as fixed, ignoring estimation uncertainty.

Purpose of the Study:

  • To develop a fully-Bayesian FPCA method, named FAST, that accounts for the uncertainty in principal component estimation.
  • To improve the stability and performance of FPCA for functional data analysis.

Main Methods:

  • FAST utilizes a projection of eigenfunctions onto an orthonormal spline basis.
  • It employs efficient sampling of the orthonormal spline coefficient matrix via a parameter expansion scheme based on polar decomposition.
  • Eigenvalues are ordered during the sampling process.

Main Results:

  • Extensive simulation studies demonstrate that FAST is highly stable.
  • FAST outperforms existing FPCA methods in performance.

Conclusions:

  • FAST provides a robust and more accurate approach to dimension reduction for functional data.
  • The method was successfully applied to analyze continuous glucose monitoring data from the DASH4D CGM study.