A1069
Title: Ultra-efficient MCMC for Bayesian longitudinal functional data analysis
Authors: Thomas Sun - Rice University (United States)
Daniel Kowal - Cornell University (United States) [presenting]
Abstract: Functional mixed models are widely useful for regression analysis with dependent functional data, including longitudinal functional data with scalar predictors. However, existing algorithms for Bayesian inference with these models only provide either scalable computing or accurate approximations to the posterior distribution, but not both. A new MCMC sampling strategy is introduced for highly efficient and fully Bayesian regression with longitudinal functional data. Using a novel blocking structure paired with an orthogonalized basis reparametrization, the algorithm jointly samples the fixed effects regression functions together with all subject- and replicate-specific random effects functions. Crucially, the joint sampler optimizes sampling efficiency for these key parameters while preserving computational scalability. Perhaps surprisingly, the new MCMC sampling algorithm even surpasses state-of-the-art algorithms for frequentist estimation and variational Bayes approximations for functional mixed models (while also providing accurate posterior uncertainty quantification), and is orders of magnitude faster than existing Gibbs samplers. Simulation studies show improved point estimation and interval coverage in nearly all simulation settings over competing approaches. The method is applied to a large physical activity dataset to study how various demographic and health factors are associated with intraday activity.
