Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Tutorial on Bayesian Functional Regression Using Stan

Ziren Jiang, Ciprian Crainiceanu, Erjia Cui

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).

Tutorial on Bayesian Functional Regression Using Stan

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).
Paper Structure (49 sections, 22 equations, 1 figure, 6 tables)

This paper contains 49 sections, 22 equations, 1 figure, 6 tables.

Table of Contents

  1. Introduction
  2. Bayesian Scalar-on-Function Regression
  3. The SoFR Model
  4. Incorporating Penalized Splines
  5. Bayesian SoFR Implementation in Stan
  6. Data preparation
  7. Stan code
  8. Reconstructing the estimated functional coefficients
  9. Simulations
  10. Data generating mechanism
  11. Competing methods
  12. Metrics
  13. Results
  14. Bayesian Functional Cox Regression
  15. The Functional Cox Regression Model
  16. ...and 34 more sections

Figures (1)

  • Figure 1: Estimated functional effect for the scalar-on-function regression for Bayesian (left) and Frequentist (right) methods. Darker gray shaded area bordered by dashed lines: pointwise $95$% confidence/credible interval. Lighter gray shaded area bordered by dotted lines: CMA $95$% confidence/credible interval.