Title: Exact Combinatorial Inference for Brain Images,
Abstract: The permutation test is known as the exact test procedure in statistics.
However, often it is not exact in practice and only an approximate method since
only a small fraction of every possible permutation is generated. Even for a
small sample size, it often requires to generate tens of thousands
permutations, which can be a serious computational bottleneck. In this paper,
we propose a novel combinatorial inference procedure that enumerates all
possible permutations combinatorially without any resampling. The proposed
method is validated against the standard permutation test in simulation studies
with the ground truth. The method is further applied in twin DTI study in
determining the genetic contribution of the minimum spanning tree of the
structural brain connectivity.