Rice-distributed autoregressive time series modeling of magnitude functional MRI data
Daniel W. Adrian, Ranjan Maitra, Daniel B. Rowe
The Annals of Applied Statistics · 2025 · Volume 19 · Issue 2
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.
Keywords
Bilateral finger-tapping motor experiment, EM algorithm, empirical information matrix, hemodynamic response function, Monte Carlo integration, Rice distribution, signal-to-noise ratio
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