Bayesian Analysis of Quasar Lightcurves with a Running Optimal Average:
  New Time Delay Measurements of COSMOGRAIL Gravitationally Lensed Quasars
  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, optimising the
ROA width, along with other model parameters, by minimising the Bayesian
Information Criterion (BIC) and sampling joint posterior parameter
distributions using MCMC methods. For analysis of quasar lightcurves, our
implementation of ROA modelling can measure time delays among lightcurves at
different wavelengths or from different images of a lensed quasar and, in
future work, be used to inter-calibrate lightcurve data from different
telescopes and estimate the shape and thus the power-density spectrum of the
lightcurve. 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 lightcurves with a prior on
the power-density spectrum. We analyse published COSMOGRAIL lightcurves of
multi-lensed quasar lightcurves and present the resulting measurements of the
inter-image time delays and detection of microlensing effects.
