Ultra-Efficient MCMC for Bayesian Longitudinal Functional Data Analysis
提出一种新的MCMC采样策略，通过联合采样固定效应和随机效应函数，在保持计算可扩展性的同时实现高效贝叶斯推断，优于现有频率派和变分贝叶斯方法，并应用于大型身体活动数据分析人口统计和健康因素与日内活动的关联。
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. We introduce a new MCMC sampling strategy for highly efficient and fully Bayesian regression with longitudinal functional data. Using a novel blocking structure paired with an orthogonalized basis reparameterization, our 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, our 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. We apply our method to a large physical activity dataset to study how various demographic and health factors associate with intraday activity. Supplementary materials for this article are available online.