A Kernel-Based Approach to Estimating Phase Shifts Between Irregularly Sampled Time Series: An Application to Gravitational Lenses

Abstract

Abstract. Given two scaled, phase shifted and irregularly sampled noisy realisations of the same process, we attempt to recover the phase shift in this contribution. We suggest a kernel-based method that directly models the underlying process via a linear combination of Gaussian kernels. We apply our method to estimate the phase shift between temporal variations, in the brightness of multiple images of the same distant gravitationally lensed quasar, from irregular but simultaneous observations of all images. In a set of controlled experiments, our method outperforms other state-of-art statistical methods used in astrophysics, in particular in the presence of realistic gaps and Gaussian noise in the data. We apply the method to actual observations (at several optical frequencies) of the doubly imaged quasar Q0957+561. Our estimates at various frequencies are more consistent than those of the currently used methods.

Computational Intelligence in Astronomy – A Win-Win Situation

“…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]. Our results were consistent with these findings.…”

Analysis of Time Series with Artificial Neural Networks

“…The problem of real data is that the definite time delay estimation for most known gravitational lens remains uncertain [3]. Even though, in this paper, we study the GRNN on artificial data.…”

“…Because the importance of the study of time delay, many efforts have been done to estimate the time delay with real and artificial data [10,12,13,8,3,5]. The problem of real data is that the definite time delay estimation for most known gravitational lens remains uncertain [3].…”

“…We compare the results on artificial data [3], where the true time delay is known and state-of-the-art methods have been tested. In the comparison, some statistics are used to measure the significance of results.…”

“…Methods to deal with the time delay problem are developed in the astrophysics literature [10,12,13,8]. Two main methods have been developed in computer science [3,5], and they employ Kernel Methods and Bayesian Estimation, respectively.…”