Bayesian adaptive selection of basis functions for functional data representation

Area of Science:

• Statistics
• Computational Statistics

Background:

• Functional data analysis requires efficient methods for representing complex data.
• Selecting appropriate basis functions is crucial for accurate functional data representation.
• Existing methods may lack adaptivity or uncertainty quantification in basis selection.

Purpose of the Study:

• To develop a new Bayesian approach for adaptive basis function selection in functional data analysis.
• To introduce a method that determines both the number and specific basis functions needed for data representation.
• To quantify the uncertainty associated with the basis selection process.

Main Methods:

• A Bayesian approach utilizing a Gibbs sampler was developed.
• Bernoulli latent variables were employed to assign zero probability to certain basis function coefficients.
• The method was applied to functional data, including daily COVID-19 cases in Brazil.

Main Results:

• The proposed methodology demonstrated accuracy in estimating coefficients.
• The procedure effectively identified the true set of basis functions in simulations.
• The method successfully handled variations due to experimental error and individual differences.

Conclusions:

• The developed Bayesian approach provides an adaptive and robust method for basis function selection in functional data analysis.
• The procedure offers valuable uncertainty quantification for the selection process.
• The method shows promise for analyzing complex, real-world functional datasets and outperforms traditional methods in certain aspects.