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Bayesian adaptive selection of basis functions for functional data representation.

Pedro Henrique T O Sousa1, Camila P E de Souza2, Ronaldo Dias1

  • 1Department of Statistics, University of Campinas, Campinas, SP, Brazil.

Journal of Applied Statistics
|March 25, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces a novel Bayesian method for selecting basis functions in functional data analysis. The approach adaptively determines the number and type of basis functions, offering uncertainty measures and handling real-world data variations.

Keywords:
Bayesian inferencebasis selectionfunctional datafunctional data analysislatent variable

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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.