Figure 9.

Statistical thresholds identified via Gaussian mixture modeling. Figure illustrates variable appearance of Gaussian mixture modeling (GMM) results using four t-statistic maps from different components (A–D). Histogram of z-scores is shown for each t-statistic map (data line), modeled as the full mixture of Gaussians density (gmm fit line), as well as by distinct Gaussian sub-distributions according to class (i.e., “null,” “activation,” “deactivation”). Probability density (y-axis) is used to determine z-score threshold(s) of statistical significance (black squares). (A) Example of more straightforward results, in which three fit curves are taken to be “deactivation” (fit 1, left-shifted with negative z-scores; dark blue line), “null” (fit 2, centrally localized near zero; green line), and “activation” (fit 3, right-shifted with positive z-scores; turquoise color line). Gray region indicates z-values with statistically insignificant BOLD activity, while yellow regions highlight z-scores beyond identified thresholds exhibiting statistically significant BOLD activity. Intercepts between fit 1 (or fit 3) with “null” (fit 2) curve, is marked with small black square. (B) Example of t-statistic histogram with only one significant positive threshold (black square intercepts), despite presence of both positive (fit 3) and negative (fit 1) distributions. Probability density of the latter never surpasses the null (fit 2), confirmed with zoomed in view (no intercept). (C) Example of “split null” distribution, with the null class modeled by fit 2 and 3. Note, only the z-score furthest from zero is considered the threshold: negative threshold (z-score = −2.645) is described when fit 1 > fit 2 (not when fit 1 > fit 3), while positive threshold (z-score = 2.768) is described when fit 4 > fit 3 (not when fit 4 > fit 2). (D) Example for more challenging interpretation of results when fit 2 (green line) can be described as right-shifted (suggestive of “activation” class) with large volume (suggestive of “null” class).