Variational Bayes Techniques for Correcting Spitzer Systematics

Accurate measurements of primary transit and secondary eclipse depths made with the Infrared Array Camera (IRAC) on board the Spitzer Space Telescope have been highly successful at characterising the atmospheres of exoplanets. In order to make these measurements, it is crucial to correct for intrapixel sensitivity variations in the 3.6um and 4.5um channels as well as a ramp-up effect in the 5.8um and 8.0um channels. This is typically done by modelling them simultaneously with a model for the planetary signal using Markov Chain Monte Carlo (MCMC) direct sampling methods. We present an alternative approach that makes use of variational Bayes (VB) techniques to directly approximate the posterior distribution, leading to dramatic improvements in computation time. This allows us to consider models with many more free parameters so that complex behaviour, if present, can be accurately captured. A powerful advantage of VB is that over-fitting is automatically avoided, without the need to resort to discriminating statistics such as the Bayesian Information Criterion (BIC). We demonstrate the approach on previously published Spitzer data.