Abstract
Scientists use high-dimensional measurement assays to detect and prioritize regions of strong signal in a spatially organized domain. Examples include finding methylation enriched genomic regions using microarrays and identifying active cortical areas using brain-imaging. The most common procedure for detecting potential regions is to group together neighboring sites where the signal passed a threshold. However, one needs to account for the selection bias induced by this opportunistic procedure to avoid diminishing effects when generalizing to a population. In this paper, we present a model and a method that permit population inference for these detected regions. In particular, we provide non-asymptotic point and confidence interval estimates for mean effect in the region, which account for the local selection bias and the non-stationary covariance that is typical of these data. Such summaries allow researchers to better compare regions of different sizes and different correlation structures. Inference is provided within a conditional one-parameter exponential family for each region, with truncations that match the constraints of selection. A secondary screening-and-adjustment step allows pruning the set of detected regions, while controlling the false-coverage rate for the set of regions that are reported. We illustrate the benefits of the method by applying it to detected genomic regions with differing DNA-methylation rates across tissue types. Our method is shown to provide superior power compared to non-parametric approaches.
