2025/12/03 by Alden Green, Green, Alden, Jonathan Taylor +1
Engineering · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Microwave Imaging and Scattering Analysis #Random Matrices and Applications #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2512.04059
openalex publication_date 2025/12/03 · openalex created_date 2025/12/05 · openalex updated_date 2026/07/28
Peak inference concerns the use of local maxima ("peaks") of a noisy random field to detect and localize regions where underlying signal is present. We propose a peak inference method that first subjects observed peaks to a significance test of the null hypothesis that no signal is present, and then uses the peaks that are declared significant to construct post-selectively valid confidence regions for the location and height of nearby true peaks. We analyze the performance of this method in a smooth signal plus constant variance noise model under a high-curvature asymptotic assumption, and prove that it asymptotically controls both the number of false discoveries, and the number of confidence regions that do not contain a true peak, relative to the number of points at which inference is conducted. An important intermediate theoretical result uses the Kac-Rice formula to derive a novel approximation to the intensity function of a point process that counts local maxima, which is second-order accurate under the alternative, nearby high-curvature true peaks.