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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
Summary
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.
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.
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