Fig. 2.

Results on simulated data comparing the hierarchical Dirichlet process with random effects and a thresholding approach. The activation clusters estimated from the hierarchical Dirichlet process with random effects are shown for datasets simulated with (a) low activation intensities with high noise level (k_m = 1.0 and ${\sigma }_{\text{act}}^2={\sigma }_{\text{bg}}^2=1.0$), and (b) high activation intensities with low noise level (k_m = 2.0 and ${\sigma }_{\text{act}}^2={\sigma }_{\text{bg}}^2=0.2$). The results are based on the single MCMC sample with the highest posterior probability. The left-most images in Panels (a) and (b) show the true locations of the template activation clusters as ‘+’s, and estimated regions within one standard deviation (as measured by the Φ_m’s) as ellipses. In the next seven images in Panels (a) and (b), the estimated image-specific activation clusters are overlaid over the raw images as ellipses of width one standard deviations (as estimated by the Σ_mj’s). ROC curves for detecting the true activation voxels averaged over 20 simulated datasets are shown for (c) varying heights k_m’s (with fixed Σ_mj), and (d) varying widths, the variance elements of Σ_mj’s, of the activation clusters (for fixed k_m). In Panels (c) and (d), the three sets of ROC curves from the left to the right correspond to the noise levels ${\sigma }_{\text{bg}}^2={\sigma }_{\text{act}}^2=0.2$, 0.6, and 1.0, respectively.