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Tutorial on Bayesian Functional Regression Using Stan.

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Summary
This summary is machine-generated.

This study introduces Bayesian functional regression models using Stan, showing comparable performance to frequentist methods. These Bayesian models offer greater flexibility and are valuable when frequentist alternatives are limited.

Keywords:
Bayesian data analysisfunctional Cox regressionfunctional data analysisfunctional principal component analysisstan

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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.