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The international journal of biostatistics
Feb 05, 2025;

Bayesian covariance regression in functional data analysis with applications to functional brain imaging.

John Shamshoian, Nicholas Marco, Damla Şentürk, Shafali Jeste, Donatello Telesca
Author Information
  1. John Shamshoian: Department of Biostatistics, University of California, Los Angeles, CA, USA.
  2. Nicholas Marco: Department of Biostatistics, University of California, Los Angeles, CA, USA.
  3. Damla Şentürk: Department of Biostatistics, University of California, Los Angeles, CA, USA.
  4. Shafali Jeste: Division of Neurology and Neurological Institute, Children's Hospital Los Angeles, Los Angeles, USA.
  5. Donatello Telesca: Department of Biostatistics, University of California, Los Angeles, CA, USA.
PMID: 39903849 DOI: 10.1515/ijb-2023-0029

Abstract

Function on scalar regression models relate functional outcomes to scalar predictors through the conditional mean function. With few and limited exceptions, many functional regression frameworks operate under the assumption that covariate information does not affect patterns of covariation. In this manuscript, we address this disparity by developing a Bayesian functional regression model, providing joint inference for both the conditional mean and covariance functions. Our work hinges on basis expansions of both the functional evaluation domain and covariate space, to define flexible non-parametric forms of dependence. To aid interpretation, we develop novel low-dimensional summaries, which indicate the degree of covariate-dependent heteroskedasticity. The proposed modeling framework is motivated and applied to a case study in functional brain imaging through electroencephalography, aiming to elucidate potential differentiation in the neural development of children with autism spectrum disorder.

Keywords

Bayesian methods covariance regression functional data neuroimaging

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Journal Article

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