Functional principal component models for sparse and irregularly spaced data by Bayesian inference

Abstract

The area of functional principal component analysis (FPCA) has seen relatively few contributions from the Bayesian inference. A Bayesian method in FPCA is developed under the cases of continuous and binary observations for sparse and irregularly spaced data. In the proposed Markov chain Monte Carlo (MCMC) method, Gibbs sampler approach is adopted to update the different variables based on their conditional posterior distributions. In FPCA, a set of eigenfunctions is suggested under Stiefel manifold, and samples are drawn from a Langevin–Bingham matrix variate distribution. Penalized splines are used to model mean trajectory and eigenfunction trajectories in generalized functional mixed models; and the proposed model is casted into a mixed-effects model framework for Bayesian inference. To determine the number of principal components, reversible jump Markov chain Monte Carlo (RJ-MCMC) algorithm is implemented. Four different simulation settings are conducted to demonstrate competitive performance against non-Bayesian approaches in FPCA. Finally, the proposed method is illustrated to the analysis of body mass index (BMI) data by gender and ethnicity.

Keywords:

• Basis functions
• birth-death moves
• penalized smoothing
• reduced rank
• Stiefel manifold

Mathematics Subject Classifications:

• 62C10
• 62R10
• 65F50

Acknowledgments

I would like to thank the Editor, the Associate Editor and the three anonymous referees of an earlier version of this article, who gave valuable advice on clarifying and explaining my ideas.

Disclosure statement

No potential conflict of interest was reported by the author.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.