A peeling algorithm for multiple testing on a random field

The optimal decision rule for testing hypothesis using observations or statistics on a two-dimensional lattice system is theoretically well-understood since Sun and Cai (J R Stat Soc Ser B (Stat Methodol) 71(2):393–424, 2009). However, its practical use still faces several difficulties that include the computation of the local index of significance (LIS). In this paper, we propose a peeling algorithm to compute the LIS, or equivalently the marginal posterior probability for the indicator of the true hypothesis for each site. We show that the proposed peeling algorithm has several advantages over the popular Markov chain Monte Carlo methods through an extensive numerical study. An application of the peeling algorithm to finding active voxels in a task-based fMRI experiment is also presented.