Selective inference for fMRI cluster-wise analysis, issues, and recommendations for template selection: A comment on Blain et al

Two permutation-based methods for simultaneous inference have recently been published on the proportion of active voxels in cluster-wise brain imaging analysis: Notip (Blain et al., 2022) and pARI (Andreella et al., 2023). Both rely on the definition of a critical vector of ordered p-values, chosen from a family of candidate vectors, but differ in how the family is defined: computed from randomization of external data for Notip, and chosen a-priori for pARI. These procedures were compared to other proposals in literature but, due to the parallel publication process, an extensive comparison between the two is missing. We provide such a comparison, highlighting that pARI can outperform Notip if the settings are selected appropriately. However, each method carries different advantages and drawbacks.