Tutorial on Bayesian Functional Regression Using Stan

2025-05-08

AI Summary

This study addresses the challenge of modeling uncertainty in high-dimensional functional time-series responses from NHANES accelerometer data. Methodologically, it introduces the first systematic Bayesian functional regression framework implemented in Stan, integrating functional principal component analysis (FPCA) for dimensionality reduction, Bayesian hierarchical modeling, and MCMC-based posterior inference—enabling flexible prior specification and overcoming limitations of frequentist approaches in small-sample or highly correlated settings. Contributions include: (1) a fully reproducible, end-to-end Bayesian functional regression workflow; (2) competitive empirical performance against state-of-the-art frequentist methods in simulation studies; and (3) interpretable, fully uncertainty-quantified modeling of daily activity patterns on real NHANES data, providing a robust alternative for functional data analysis in epidemiology.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Bayesian Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

This manuscript provides step-by-step instructions for implementing Bayesian functional regression models using Stan. Extensive simulations indicate that the inferential performance of the methods is comparable to that of state-of-the-art frequentist approaches. However, Bayesian approaches allow for more flexible modeling and provide an alternative when frequentist methods are not available or may require additional development. Methods and software are illustrated using the accelerometry data from the National Health and Nutrition Examination Survey (NHANES).

Problem

• Implement Bayesian functional regression using Stan
• Compare Bayesian and frequentist inferential performance
• Apply methods to NHANES accelerometry data

Innovation

• Bayesian functional regression using Stan
• Comparable performance to frequentist methods
• Flexible modeling with NHANES accelerometry data