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.