A Bayesian Approach to Astronomical Time Delay Estimations

  • Mariko KimuraEmail author
  • Hyungsuk Tak
  • Taichi Kato
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)


Time delay estimations between two time series data in astronomy have some difficulties due to their sparseness. We propose a fully Bayesian method based on a state–space model for this kind of analyses, and raise one example of the application to astronomical data. Our estimation can deal with heteroskedastic observational errors of astronomical time series and has much smaller errors than the result with a conventional method. This method may be applicable for many kinds of black hole systems and has a potential to derive the information of geometrical structure of astronomical objects after some improvements.


Bayesian inference State–space model Accretion Black hole physics 



We are thankful to many amateur observers in the VSNET (Variable Star Network) team and AAVSO team ( and the CRTS ( for providing a lot of data used in this study. We also thank the INTEGRAL groups for making the products of the ToO data publicly available online at the INTEGRAL Science Data Centre. This work was financially supported by the Grant-in-Aid for JSPS Fellows for young researchers (MK) and by the Grant-in-Aid “Initiative for High-Dimensional Data-Driven Science through Deepening of Sparse Modeling” from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan (25120007, TK). Hyungsuk Tak acknowledges partial support from the United States National Science Foundation grants DMS 1127914 and DMS 1638521 given to Statistical and Applied Mathematical Sciences Institute.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Astronomy, Graduate School of ScienceKyoto UniversityKyotoJapan
  2. 2.Department of Applied and Computational Mathematics and StatisticsUniversity of Notre DameNotre DameUSA

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