Multiple testing of local maxima for detection of peaks on the (celestial) sphere

Dan Cheng, Valentina Cammarota, Yabebal Fantaye, Domenico Marinucci, Armin Schwartzman

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

We present a topological multiple testing scheme for detecting peaks on the sphere under isotropic Gaussian noise, where tests are performed at local maxima of the observed field filtered by the spherical needlet transform. Our setting is different from the standard Euclidean large domain asymptotic framework, yet highly relevant to realistic experimental circumstances for some important areas of application in astronomy, namely point-source detection in cosmic Microwave Background radiation (CMB) data. Motivated by this application, we shall 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.

Original languageEnglish (US)
Pages (from-to)31-60
Number of pages30
JournalBernoulli
Volume26
Issue number1
DOIs
StatePublished - Jan 1 2020
Externally publishedYes

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Keywords

  • CMB
  • False discovery rate
  • Gaussian random fields
  • Height distribution
  • Needlet transform
  • Overshoot distribution
  • Power
  • Sphere

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

Cheng, D., Cammarota, V., Fantaye, Y., Marinucci, D., & Schwartzman, A. (2020). Multiple testing of local maxima for detection of peaks on the (celestial) sphere. Bernoulli, 26(1), 31-60. https://doi.org/10.3150/18-BEJ1068