  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.
