Tutorial on Bayesian Functional Regression Using Stan

Area of Science:

• Statistics
• Biostatistics
• Computational Statistics

Background:

• Functional regression models are essential for analyzing data where observations are functions.
• Bayesian methods offer advantages in flexibility and incorporating prior information.
• Frequentist approaches are widely used but may have limitations in complex scenarios.

Purpose of the Study:

• To provide practical, step-by-step guidance for implementing Bayesian functional regression models.
• To compare the performance of Bayesian functional regression with existing frequentist methods.
• To demonstrate the utility of these models using real-world data.

Main Methods:

• Implementation of Bayesian functional regression models utilizing the Stan probabilistic programming language.
• Extensive simulation studies to assess inferential performance.
• Application to accelerometry data from the National Health and Nutrition Examination Survey (NHANES).

Main Results:

• Bayesian functional regression models demonstrate inferential performance comparable to state-of-the-art frequentist approaches.
• Simulations confirm the reliability and accuracy of the proposed Bayesian methods.
• The models successfully analyze complex functional data, such as accelerometry measurements.

Conclusions:

• Bayesian functional regression models offer a flexible and powerful alternative to frequentist methods.
• These models are particularly useful when frequentist approaches are unavailable or require further development.
• The provided framework and software facilitate the application of Bayesian functional regression in diverse research areas.