Rice-Distributed Autoregressive Time Series Modeling of Magnitude Functional MRI Data

Authors

Daniel W. Adrian, Grand Valley State University
Ranjan Maitra, Iowa State University
Daniel B. Rowe, Marquette UniversityFollow

Document Type

Article

Publication Date

6-2025

Publisher

Institute of Mathematical Statistics

Source Publication

Annals of Applied Statistics

Source ISSN

1932-6157

Original Item ID

DOI: 10.1214/24-aoas1981

Abstract

Functional magnetic resonance imaging (fMRI) data generally consist of time series image volumes of the magnitude of complex-valued observations at each voxel. However, incorporating Gaussian-based time series models and the Rice distribution—a more accurate model for the data—in the time series have been separated by a distributional “mismatch.” We bridge this gap by including pth-order autoregressive (AR) errors into the Gaussian model for the latent real and imaginary components underlying the Rice-distributed magnitude data. Parameter estimation is then done by augmenting the observed magnitude data with the missing phase data in an expectation-maximization (EM) algorithm framework and followed by AR order determination and computation of test statistics for activation detection. Using simulated and experimental low-SNR fMRI data, we compare the performance of this Ricean time series model with a Gaussian AR(p) model for the magnitude data and also with a complex Gaussian time series model for the entire complex-valued data. Our results show improved parameter estimation and activation detection under the Ricean AR(p) model for the magnitude data than its Gaussian counterpart. The model using the complex-valued data (which is rarely collected in practice) detects activation better than both magnitude-only models but only because it has more data. Thus, while our results here provide for the improved analysis of commonly-collected and archived magnitude-only fMRI datasets, they also argue strongly against the currently routine practice of discarding the phase of the complex-valued fMRI time series, advocating instead for their inclusion in the analysis.

Comments

Annals of Applied Statistics, Vol. 19, No. 2 (June 2025): 1494-1513. DOI.

Recommended Citation

Adrian, Daniel W.; Maitra, Ranjan; and Rowe, Daniel B., "Rice-Distributed Autoregressive Time Series Modeling of Magnitude Functional MRI Data" (2025). Mathematical and Statistical Science Faculty Research and Publications. 163.
https://epublications.marquette.edu/math_fac/163