Bayesian function-on-function regression for multilevel functional data.

Area of Science:

• Biostatistics
• Functional Data Analysis
• Medical Research

Background:

• Medical research increasingly generates complex, high-dimensional data, including finely sampled functional data (curves).
• Repeated functional measures per individual are common, necessitating methods to analyze relationships between multiple functional variables.
• Existing statistical models often struggle with the complexity and high dimensionality of such repeated functional data.

Purpose of the Study:

• To propose a general function-on-function regression model tailored for repeatedly sampled functional data on a fine grid.
• To introduce a comprehensive mixed-model framework and functional Bayesian inferential procedures.
• To address the challenge of analyzing relationships between two functional variables in complex datasets.

Main Methods:

• Development of a simple function-on-function regression model.
• Extension to a more extensive mixed-model framework for repeated functional measures.
• Implementation of functional Bayesian inferential procedures, including methods for multiple testing.

Main Results:

• The proposed models were evaluated through simulation studies to assess their performance.
• A real-world data analysis was conducted using event-related potential data.
• The study demonstrated the utility of the models in examining brain processing of images.

Conclusions:

• The developed function-on-function regression models provide a flexible and robust approach for analyzing repeated functional data.
• Functional Bayesian inference offers effective methods for handling multiple testing in complex data.
• These methods are applicable to various fields, including medical and public health research involving high-dimensional functional data.