The 2015 Paris Climate Agreement and Global Methane Pledge formalized agreement for countries to report and reduce methane emissions to mitigate near-term climate change. Emission inventories generated through surface activity measurements are reported annually or bi-annually, and evaluated periodically through a “Global Stocktake.” Emissions inverted from atmospheric data support evaluation of reported inventories, but their systematic use is stifled by spatially variable biases from prior errors combined with limited sensitivity of observations to emissions (also called smoothing error), as-well-as poorly characterized information content. Here, we demonstrate a Bayesian, optimal estimation (OE) algorithm for evaluating a state-of-the-art inventory (EDGAR v6.0) using satellite-based emissions from 2009 to 2018. The OE algorithm quantifies the information content (uncertainty reduction, sectoral attribution, spatial resolution) of the satellite-based emissions and disentangles the effect of smoothing error when comparing to an inventory. We find robust differences between satellite and EDGAR for total livestock, rice, and coal emissions: 14 ± 9, 12 ± 8, −11 ± 6 Tg CH4/yr respectively. EDGAR and satellite agree that livestock emissions are increasing (0.25–1.3 Tg CH4/yr/yr), primarily in the Indo-Pakistan region, sub-tropical Africa, and the Southern Brazilian; East Asia rice emissions are also increasing, highlighting the importance of agriculture on the atmospheric methane growth rate. In contrast, low information content for the waste and fossil emission trends confounds comparison between EDGAR and satellite; increased sampling and spatial resolution of satellite observations are therefore needed to evaluate reported changes to emissions in these sectors. Plain Language Summary The Bayesian inverse estimation algorithms we describe here, developed previously to quantify atmospheric composition from observations of Earth's radiation, is applied one step further to quantify emissions using satellite atmospheric methane data and compare them to a reported inventory. These same algorithms allow us to quantify when this comparison is informative (total uncertainty is reduced) and when it is not. Deployment of these methods will become increasingly critical to use with the ever increasing number of satellite greenhouse gas observations and their utility not just for understanding the global carbon cycle, but for informing policy about best approaches for reducing emissions to mitigate climate change.