Bayesian analysis of quasar light curves with a running optimal average: new time delay measurements of COSMOGRAIL gravitationally lensed quasars

Abstract

ABSTRACT We present a new method of modelling time-series data based on the running optimal average (ROA). By identifying the effective number of parameters for the ROA model, in terms of the shape and width of its window function and the times and accuracies of the data, we enable a Bayesian analysis, optimizing the ROA width, along with other model parameters, by minimizing the Bayesian information criterion (BIC) and sampling joint posterior parameter distributions using MCMC methods. For analysis of quasar light curves, our implementation of ROA modelling can measure time delays among light curves at different wavelengths or from different images of a lensed quasar and, in future work, be used to inter-calibrate light-curve data from different telescopes and estimate the shape and thus the power-density spectrum of the light curve. Our noise model implements a robust treatment of outliers and error-bar adjustments to account for additional variance or poorly quantified uncertainties. Tests with simulated data validate the parameter uncertainty estimates. We compare ROA delay measurements with results from cross-correlation and from javelin, which models light curves with a prior on the power-density spectrum. We analyse published COSMOGRAIL light curves of multilensed quasar light curves and present the resulting measurements of the inter-image time delays and detection of microlensing effects.