Title: Multiple testing of local maxima for detection of peaks on the (celestial) sphere
Authors: Armin Schwartzman - University of California, San Diego (United States) [presenting]
Dan Cheng - Texas Tech University (United States)
Valentina Cammarota - Sapienza University of Rome (Italy)
Yabebal Fantaye - African Institute for Mathematical Sciences (South Africa)
Domenico Marinucci - University of Rome Tor Vergata (Italy)
Abstract: A topological multiple testing scheme for detecting peaks on the sphere under isotropic Gaussian noise is presented. The tests are performed at local maxima of the observed field filtered by the spherical needlet transform. Motivated by point-source detection in cosmic Microwave Background radiation (CMB) data, we focus on cases where a single realization of a smooth isotropic Gaussian random field on the sphere is observed, and a number of well-localized signals are superimposed on such background field. The proposed algorithms, combined with the Benjamini-Hochberg procedure for thresholding $p$-values, provide asymptotic control of the False Discovery Rate (FDR) and power consistency as the signal strength and the frequency of the needlet transform get large.