Statistical mapping of normative or pathological changes in the brain is of utmost importance for our understanding of its structure and function. Mass-univariate as well as multivariate pattern analysis techniques have been proposed to map group differences in neuroimaging studies. However, these methods often suffer from low sensitivity and specificity, as well as high computational cost. To address these limitations, we introduce a novel multivariate statistical framework, termed MIDAS, aiming to efficiently produce highly sensitive and specific statistical brain maps. MIDAS utilizes localized discriminative learning to produce a statistic whose significance can be assessed by analytic approximation of permutation testing. Discriminative learning allows for finding the optimal adaptive filtering of the image for group analysis. The null distribution of the resulting statistic is analytically approximated, which provides computational efficiency. MIDAS is extensively validated using simulated atrophy on structural magnetic resonance images of 200 healthy subjects. Furthermore, the applicability of MIDAS to clinical studies is confirmed by applying it to an Alzheimer's disease (AD) dataset (ADNI) comprising 199 AD patients and 230 controls.