Bayesian Estimation of Time Delays Between Unevenly Sampled Signals

A method for estimating time delays between signals that are irregularly sampled is presented. The approach is based on postulating a latent variable model from which the observed signals have been generated and computing the posterior distribution of the delay. This is achieved partly by exact marginalisation and partly by using MCMC methods. Experiments with artificial data show the effectiveness of the proposed approach while results with real-world gravitational lens data provide the main motivation for this work.

[1]  E. Jaynes.  Probability theory : the logic of science , 2003 .

[2]  Bernard F. Burke,et al.  The radio time delay in the double quasar 0957 + 561 , 1992 .

[3]  Robert B. Ash,et al.  Information Theory , 2020, The SAGE International Encyclopedia of Mass Media and Society.

[4]  David J. C. MacKay,et al.  Information Theory, Inference, and Learning Algorithms , 2004, IEEE Transactions on Information Theory.

[5]  K. Gebhardt,et al.  The Quadruple Gravitational Lens PG 1115+080: Time Delays and Models , 1996, astro-ph/9611051.

[6]  Peter Tiño,et al.  How accurate are the time delay estimates in gravitational lensing? , 2006, ArXiv.

[7]  J. Pelt,et al.  Time delay controversy on QSO 0957+561 not yet decided , 1994 .

[8]  P. N. Wilkinson,et al.  Time delay for the gravitational lens system B0218+357 , 1998, astro-ph/9811282.

[9]  D. Long,et al.  A Robust Determination of the Time Delay in 0957+561A, B and a Measurement of the Global Value of Hubble's Constant , 1996, astro-ph/9610162.

[10]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[11]  R Edelson,et al.  The Discrete Correlation Function: a New Method for Analyzing Unevenly Sampled Variability Data , 1988 .

[12]  S. Refsdal.  On the possibility of determining Hubble's parameter and the masses of galaxies from the gravitational lens effect , 1964 .

[13]  Andrew Gelman,et al.  General methods for monitoring convergence of iterative simulations , 1998 .

[14]  Rennan Barkana,et al.  Analysis of Time Delays in the Gravitational Lens PG 1115+080 , 1997, astro-ph/9701068.

[15]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .