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ROA (Running Optimal Average) describes time series data. This model uses a Gaussian window function that moves through the data giving stronger weights to points close to the center of the Gaussian. Therefore, the width of the window function, delta, controls the flexibility of the model, with a small delta providing a very flexible model. The function also calculates the effective number of parameters, as a very flexible model will correspond to large number of parameters while a rigid model (low delta) has a low effective number of parameters. Knowing the effective number of parameters can be used to optimize the window width, e.g., using the Bayesian information criterion (BIC). An error envelope, which expands appropriately where there are gaps in the data, is also calculated for the model.
PyROA models quasar light curves where the variability is described using a running optimal average (ROA), and parameters are sampled using Markov Chain Monte Carlo (MCMC) techniques using emcee (ascl:1303.002). Using a Bayesian approach, priors can be used on the sampled parameters. Currently it has three main uses: 1.) Determining the time delay between lightcurves at different wavelengths; 2.) Intercalibrating light curves from multiple telescopes, merging them into a single lightcurve; and 3.) Determining the time delay between images of lensed quasars, where the microlensing effects are also modeled. PyROA also includes a noise model, where there is a parameter for each light curve that adds extra variance to the flux measurments, to account for underestimated errors; this can be turned off if required. Example jupyter notebooks that demonstrate each of the three main uses of the code are provided.