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

Shamshoian John (), Marco Nicholas (), Şentürk Damla (), Jeste Shafali () and Telesca Donatello ()
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Shamshoian John: Department of Biostatistics, University of California, Los Angeles, CA, USA
Marco Nicholas: Department of Biostatistics, University of California, Los Angeles, CA, USA
Şentürk Damla: Department of Biostatistics, University of California, Los Angeles, CA, USA
Jeste Shafali: Division of Neurology and Neurological Institute, Children’s Hospital Los Angeles, Los Angeles, USA
Telesca Donatello: Department of Biostatistics, University of California, Los Angeles, CA, USA

The International Journal of Biostatistics, 2025, vol. 21, issue 1, 115-128

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 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1515/ijb-2023-0029

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