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

  • John Shamshoian , Nicholas Marco , Damla Şentürk , Shafali Jeste and Donatello Telesca EMAIL logo
Published/Copyright: February 5, 2025
The International Journal of Biostatistics
From the journal The International Journal of Biostatistics Volume 21 Issue 1

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
Corresponding author: Donatello Telesca, Department of Biostatistics, University of California, Los Angeles, CA, USA, E-mail: 

Funding source: National Institute of Mental Health

Award Identifier / Grant number: R01 MH122428-01

  1. Research ethics: Data was analyzed under UCLA IRB#20-000029 [Senturk PI] – granted 2/14/2022.

  2. Informed consent: Not applicable.

  3. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest: All other authors state no conflict of interest.

  6. Research funding: Our research was supported by the National Institute of Mental Health grant- NIMH: R01 MH122428-01.

  7. Data availability: Data is available upon request from Shafali Jeste [sjeste@chla.usc.edu].

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Supplementary Material

This article contains supplementary material (https://doi.org/10.1515/ijb-2023-0029).

Received: 2023-02-16
Accepted: 2025-01-07
Published Online: 2025-02-05

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/ijb-2023-0029
Keywords for this article
Bayesian methods; covariance regression; functional data; neuroimaging

Articles in the same Issue

  1. Frontmatter
  2. Research Articles
  3. Prognostic adjustment with efficient estimators to unbiasedly leverage historical data in randomized trials
  4. Homogeneity test and sample size of response rates for AC 1 in a stratified evaluation design
  5. A review of survival stacking: a method to cast survival regression analysis as a classification problem
  6. DsubCox: a fast subsampling algorithm for Cox model with distributed and massive survival data
  7. A hybrid hazard-based model using two-piece distributions
  8. Regression analysis of clustered current status data with informative cluster size under a transformed survival model
  9. Bayesian covariance regression in functional data analysis with applications to functional brain imaging
  10. Risk estimation and boundary detection in Bayesian disease mapping
  11. An improved estimator of the logarithmic odds ratio for small sample sizes using a Bayesian approach
  12. Short Communication
  13. A multivariate Bayesian learning approach for improved detection of doping in athletes using urinary steroid profiles
  14. Research Articles
  15. Guidance on individualized treatment rule estimation in high dimensions
  16. Weighted Euclidean balancing for a matrix exposure in estimating causal effect
  17. Penalized regression splines in Mixture Density Networks
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