Efficient moments-based permutation tests: A framework, methods and applications

Multiple hypotheses testing is widely used in biomedical image analysis. With unknown distribution and small sample size of the data, existing multiple testing involves testing thousands of hypotheses for statistically significant effects through permutation. The factorial scale computation cost becomes a bottleneck in the real applications.;In this work, we develop an efficient moments-based permutation test approach to improve the system's efficiency by approximating the permutation distribution of the test statistic with Pearson distribution series, which involves the calculation of the first four moments of the permutation distribution. We thus propose a novel recursive method to derive these moments theoretically and analytically without any permutation. Detailed derivations and experimental results using different test statistics are demonstrated using simulated data and real applications. The proposed strategy takes advantage of nonparametric permutation tests and parametric Pearson distribution approximation to achieve both accuracy/flexibility and efficiency.;The key and only assumption for permutation tests is data exchangeability. In real applications, the data exchangeability condition is not always valid. In order to preserve the exchangeability condition required in permutation tests, we propose a new blockwise permutation test approach based on the moments of the test statistic. The accuracy and efficiency of the proposed method are demonstrated through simulated experiments and magnetic resonance imaging (MRI) brain data, including the multi-site voxel-based morphometry analysis from structural MRI (sMRI) and activation detection from functional MRI (fMRI).