Hi Falko,
You’re raising a controversial and challenging issue in neuroimaging. While the dominant view in the field has favored stringent multiple testing adjustments, I tend to disagree with both the underlying assumptions and the methodological approach.
The prevailing modeling strategy, massive univariate analysis, treats each voxel independently, assuming no shared information across the brain. This assumption is fundamentally flawed and gives rise to the multiple testing problem. Although many adjustment methods attempt to account for local spatial structure via smoothness, the resulting penalties are often excessively conservative.
For this reason, we advocate for a "highlight, but don’t hide" approach in reporting results. You can find more discussion in this blog post and this video recording. This reporting strategy is also advocated in a recent publication and a recent preprint.
Ideally, multiple testing should be addressed through hierarchical modeling. We’ve demonstrated a proof of concept at the region level in this paper, and we hope to extend this framework to voxel-wise analysis in future work.
Gang Chen