Cluster Size Matters: A Comparative Study of Notip and pARI for Post Hoc Inference in fMRI

All Resolutions Inference (ARI) is a post hoc inference method for functional Magnetic Resonance Imaging (fMRI) data analysis that provides valid lower bounds on the proportion of truly active voxels within any, possibly data-driven, cluster. As such, it addresses the paradox of spatial specificity encountered with more classical cluster-extent thresholding methods. It allows the cluster-forming threshold to be increased in order to locate the signal with greater spatial precision without overfitting, also known as the drill-down approach. Notip and pARI are two recent permutation-based extensions of ARI designed to increase statistical power by accounting for the strong dependence structure typical of fMRI data. A recent comparison between these papers based on large voxel clusters concluded that pARI outperforms Notip. We revisit this conclusion by conducting a systematic comparison of the two. Our reanalysis of the same fMRI data sets from the Neurovault database demonstrates the existence of complementary performance regimes: while pARI indeed achieves higher sensitivity for large clusters, Notip provides more informative and robust results for smaller clusters. In particular, while Notip supports informative ``drill-down'' exploration into subregions of activation, pARI often yields non-informative bounds in such cases, and can even underperform the baseline ARI method.