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Toward the detection of gravitational waves under non-Gaussian noises I. Locally optimal statistic

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      After reviewing the standard hypothesis test and the matched filter technique to identify gravitational waves under Gaussian noises, we introduce two methods to deal with non-Gaussian stationary noises. We formulate the likelihood ratio function under weakly non-Gaussian noises through the Edgeworth expansion and strongly non-Gaussian noises in terms of a new method we call Gaussian mapping where the observed marginal distribution and the two-body correlation function are fully taken into account. We then apply these two approaches to Student’s t-distribution which has a larger tails than Gaussian. It is shown that while both methods work well in the case the non-Gaussianity is small, only the latter method works well for highly non-Gaussian case.

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      [*1 ]Research Center for the Early Universe (RESCEU), Graduate School of Science, The University of Tokyo, Tokyo, Japan.
      [*2 ]Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), TODIAS, WPI, The University of Tokyo, Kashiwa, Chiba, Japan.
      Author notes
      []Correspondence should be addressed: J. Yokoyama, Research Center for the Early Universe (RESCEU), Graduate School of Science, The University of Tokyo, 113-0033, Japan (e-mail: yokoyama@ ).

      (Communicated by Yoshihide KOZAI, M.J.A.)

      Proc Jpn Acad Ser B Phys Biol Sci
      Proc. Jpn. Acad., Ser. B, Phys. Biol. Sci
      Proceedings of the Japan Academy. Series B, Physical and Biological Sciences
      The Japan Academy (Tokyo, Japan )
      11 December 2014
      : 90
      : 10
      : 422-432
      25504231 4335139 pjab-90-422 10.2183/pjab.90.422
      © 2014 The Japan Academy

      This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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