The field of exoplanet atmospheric characterization is trending towards comparative studies involving many planets, and using hierarchical modelling is a natural next step. Here we demonstrate two use cases. We first use hierarchical modelling to quantify variability in repeated observations, by reanalyzing a suite of ten Spitzer secondary eclipse observations of the hot Jupiter XO-3b. We compare three models: one where we fit ten separate eclipse depths, one where we use a single eclipse depth for all ten observations, and a hierarchical model. By comparing the Widely Applicable Information Criterion (WAIC) of each model, we show that the hierarchical model is preferred over the others. The hierarchical model yields less scatter across the suite of eclipse depths, and higher precision on the individual eclipse depths, than does fitting the observations separately. We do not detect appreciable variability in the secondary eclipses of XO-3b, in line with other analyses. Finally, we fit the suite of published dayside brightness measurements from Garhart (2020) using a hierarchical model. The hierarchical model gives tighter constraints on the individual brightness temperatures and is a better predictive model, according to the WAIC. Notably, we do not detect the increasing trend in brightness temperature ratios versus stellar irradiation reported by Garhart (2020) and Baxter (2020). Although we tested hierarchical modelling on Spitzer eclipse data of hot Jupiters, it is applicable to observations of smaller planets like hot neptunes and super earths, as well as for photometric and spectroscopic transit or phase curve observations.
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