A Bayesian Complex-Valued Latent Variable Model Applied to Functional Magnetic Resonance Imaging
Document Type
Article
Publication Date
1-2025
Publisher
Oxford University Press
Source Publication
Journal of the Royal Statistical Society, Series C: Applied Statistics
Source ISSN
0035-9254
Original Item ID
DOI: 10.1093/jrsssc/qlae046
Abstract
In linear regression, the coefficients are simple to estimate using the least squares method with a known design matrix for the observed measurements. However, real-world applications may encounter complications such as an unknown design matrix and complex-valued parameters. The design matrix can be estimated from prior information but can potentially cause an inverse problem when multiplying by the transpose as it is generally ill-conditioned. This can be combat by adding regularizers to the model but does not always mitigate the issues. Here, we propose our Bayesian approach to a complex-valued latent variable linear model with an application to functional magnetic resonance imaging (fMRI) image reconstruction. The complex-valued linear model and our Bayesian model are evaluated through extensive simulations and applied to experimental fMRI data.
Recommended Citation
Sakitis, Chase J.; Brown, D. Andrew; and Rowe, Daniel B., "A Bayesian Complex-Valued Latent Variable Model Applied to Functional Magnetic Resonance Imaging" (2025). Mathematical and Statistical Science Faculty Research and Publications. 156.
https://epublications.marquette.edu/math_fac/156
Comments
Journal of the Royal Statistical Society, Series C: Applied Statistics, Vol. 74, No. 1 (January 2025): 100-125. DOI.