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.
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Saha, P.: Gravitational Lensing. Encyclopedia of Astronomy and Astrophysics (2000)
Kochanek, C., Schechter, P.: The Hubble constant from gravitational lens time delays. Carnegie Observatories Astrophysics Series 2 (2004)
Pelt, J., Kayser, R., Refsdal, S., Schramm, T.: Time delay controversy on QSO 0957+561 not yet decided. Astronomy and Astrophysics 286(1), 775–785 (1994)
Pelt, J., Kayser, R., Refsdal, S., Schramm, T.: The light curve and the time delay of QSO 0957+561. Astronomy and Astrophysics 305(1), 97–106 (1996)
Kundic, T., Turner, E., Colley, W., Gott-III, J., Rhoads, J., Wang, Y., Bergeron, L., Gloria, K., Long, D., Malhorta, S., Wambsganss, J.: A robust determination of the time delay in 0957+561A,B and a measurement of the global value of Hubble’s constant. Astrophysical Journal 482(1), 75–82 (1997)
Ovaldsen, J., Teuber, J., Schild, R., Stabell, R.: New aperture photometry of QSO 0957+561; application to time delay and microlensing. Astronomy and Astrophysics 402(3), 891–904 (2003)
Cuevas-Tello, J., Tiňo, P., Raychaudhury, S.: How accurate are the time delay estimates in gravitational lensing? Astronomy and Astrophysics (accepted, 2006), http://arxiv.org/abs/astro-ph/0605042
Eigenbrod, A., Courbin, F., Vuissoz, C., Meylan, G., Saha, P., Dye, S.: COSMOGRAIL: The COSmological MOnitoring of GRAvItational Lenses. I. How to sample the light curves of gravitationally lensed quasars to measure accurate time delays. Astronomy and Astrophysics 436, 25–35 (2005)
Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer, Heidelberg (2001)
Shawe-Taylor, J., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press, Cambridge (2004)
Press, H., Flannery, B., Teukolsky, S., Vetterling, W.: Numerical Recipes. Cambridge University Press, Cambridge (1986)
Golub, G.H., Van Loan, C.F.: Matrix Computations, 2nd edn. The Johns Hopkins University Press (1989)
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Cuevas-Tello, J.C., Tiňo, P., Raychaudhury, S. (2006). A Kernel-Based Approach to Estimating Phase Shifts Between Irregularly Sampled Time Series: An Application to Gravitational Lenses. In: Fürnkranz, J., Scheffer, T., Spiliopoulou, M. (eds) Machine Learning: ECML 2006. ECML 2006. Lecture Notes in Computer Science(), vol 4212. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11871842_59
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DOI: https://doi.org/10.1007/11871842_59
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