A corrected full-run contrast score had lower variance in 431 AOMIC designs under correct Gaussian models with known row covariance

We tested corrected squared contrast scores with 431 public AOMIC working-memory designs. The mean model was correct and fixed. Noise was Gaussian, with separable row and feature covariance. The row covariance was known. The spatial metric and row weights were fixed. Under these assumptions, we proved that the corrected full-run GLS score was a conditional mean of each corrected same-run split product. Thus its variance and mean squared error were no larger. We derived exact variances that include dependence from the shared residual correction. All 5,172 tested pair comparisons had lower full-score variance at four assumed signal levels. For white noise and consecutive halves with a shared filter, median null variance fell by 60.68% in PIOP1 and 60.52% in PIOP2. Checks used dense matrix formulas, separate numerical solvers, 480,000 simulated responses, and conditional residual rotations. A clean offline rebuild reproduced eight finite design result files and all weight arrays exactly. A secondary check showed that a wrong row covariance can bias the full score. No BOLD image was used. The package contains the proof, calculator, source code, selected inputs, source hashes, results, and rebuild instructions. This study does not test a benefit in measured brain images or over independent-run methods.

contrast estimation · generalized least squares · variance reduction · Rao-Blackwellization · functional MRI · Gaussian models · row covariance · AOMIC