B1048
Title: Robust Bayesian functional principal component analysis
Authors: Liangliang Wang - Simon Fraser University (Canada) [presenting]
Jiarui Zhang - Simon Fraser University (Canada)
Jiguo Cao - Simon Fraser University (Canada)
Abstract: A robust Bayesian functional principal component analysis (FPCA) is developed by incorporating skew elliptical classes of distributions. The proposed method effectively captures the primary source of variation among curves, even when abnormal observations contaminate the data. The observations are modeled using skew elliptical distributions by introducing skewness with transformation and conditioning into the multivariate elliptical symmetric distribution. To recast the covariance function, an approximate spectral decomposition is employed. The selection of prior specifications is discussed and detailed information on posterior inference is provided, including the forms of the full conditional distributions, choices of hyperparameters, and model selection strategies. Furthermore, the model is extended to accommodate sparse functional data with only a few observations per curve, thereby creating a more general Bayesian framework for FPCA. To assess the performance of the proposed model, simulation studies are conducted comparing it to well-known frequentist methods and conventional Bayesian methods. The results demonstrate that the method outperforms existing approaches in the presence of outliers and performs competitively in outlier-free datasets. Furthermore, the effectiveness of the method is illustrated by applying it to environmental and biological data to identify outlying functional data.
