Another attempt at using Gaussian processes to model time series, I’m looking at light curves from active galactic nuclei (AGN). The key thing I’m trying to do here is find and model flaring events.

First, I was interested to see if I could spot outliers representing the peaks of flares, while using a Gaussian processes (GP) model for background variability. The document below shows that attempt. The red band in each plot shows the GP prediction if there were no significant outliers, while the red dots show the outliers. (BTW, the way I embedded the code is very klunky but explained here.)

[gview file=”http://www.astrojack.com/wp-content/uploads/2015/03/looking_for_outliers.pdf”]

Next, I wanted to try to fit one of the apparent flaring events with a model that allowed for correlated noise. To that end, I adapted the example from Foreman-Mackey’s george python module. My solution is shown below. I need to incorporate a variable number of flaring events (I only allowed one for this example), but the model fit worked pretty well. In the second plot below, the blue band shows the range of model fits from the Markov-Chain Monte-Carlo (MCMC) analysis.

[gview file=”http://www.astrojack.com/wp-content/uploads/2015/03/fit_using_GP.pdf”]