Probabilistic Modelling for Delay Estimation in Gravitationally Lensed Photon Streams

  • Sultanah Al Otaibi
  • Peter Tiňo
  • Somak Raychaudhury
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9937)

Abstract

We test whether a more principled treatment of delay estimation in lensed photon streams, compared with the standard kernel estimation method, can have benefits of more accurate (less biased) and/or more stable (less variance) estimation. To that end, we propose a delay estimation method in which a single latent inhomogeneous Poisson process underlying the lensed photon streams is imposed. The rate function model is formulated as a linear combination of nonlinear basis functions. Such unifying rate function is then used in delay estimation based on the corresponding Innovation Process. This method is compared with a more straightforward and less principled baseline method based on kernel estimation of the rate function. Somewhat surprisingly, the overall emerging picture is that the theoretically more principled method does not bring much practical benefit in terms of the bias/variance of the delay estimation. This is in contrast to our previous findings on daily flux data.

Keywords

Gravitational lensing Non-homogeneous Poisson process Kernel estimation methods 

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Sultanah Al Otaibi
    • 1
    • 2
  • Peter Tiňo
    • 1
  • Somak Raychaudhury
    • 3
    • 4
    • 5
  1. 1.School of Computer ScienceUniversity of BirminghamBirminghamUK
  2. 2.College of Computer and Information SciencesKing Saud UniversityRiyadhSaudi Arabia
  3. 3.School of Physics and AstronomyUniversity of BirminghamBirminghamUK
  4. 4.Inter-University Centre for Astronomy and AstrophysicsPuneIndia
  5. 5.Department of PhysicsPresidency UniversityKolkataIndia

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