Bayesian estimation of time delays between unevenly sampled signals

Abstract

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.

Computational Intelligence in Astronomy – A Win-Win Situation

“…After tests for statistical significance, the machine learning based method employing kernel regression emerged as a clear overall winner in the large set of controlled experiments on synthetic data with known time delay. We stress that this method was able to sometimes outperform even methods that were used to generate the data sets themselves (Gaussian process or the Bayesian model of [13]). In terms of real data from Q0957+561, the best (smallest estimated error) time delay quotes were 417±3 [18] and 419.5±0.8 [6].…”

“…Indeed, a major problem with time delay estimation in astrophysics literature has been that these estimates are routinely produced for individual quasars, for which we have no idea what the 'true' time delay is (e.g. [30,28,3,7,13]). The uncertainty bounds in the reported estimates are mostly due to assumed noise model on the observationsthe estimation has been repeated in a series of Monte Carlo experimental data generated from the measured flux values, under the noise model.…”

“…We imposed seven 'true' delays and 100 realisations for each value of true delay [5]. -The data was generated from a Bayesian model [13], simulating three levels of noise with 225 data sets per level of noise (there were 3 levels of noise). The data were irregularly sampled with 100 observations per time series.…”

A novel online adaptive time delay identification technique

“…Hence, from (12), it follows that q(·) ∈ L ∞ . Since a * (t) is a function of the bounded signals, and q(·) is a measurable bounded signal, from (16), it follows that . q f (t) ∈ L ∞ .…”

“…Govindan et al [15] showed that the coherence analysis is suitable for time delay identification of narrow band coherence signals for which the conventional methods can not be reliably applied and used the method to identify time delay between two simultaneously measured signals. In [16], Harva and Raychaudhury proposed a Bayesian approach for identifying time delay between signals that are irregularly sampled. Bhardwaj and Nath [17] proposed a maximum likelihood identifier for time delay associated with each path in a multipath acoustic channel.…”