AbstractAtmospheric methane observations are used to test methane emission inventories as the sum of emissions should correspond to observed methane concentrations. Typically, concentrations are inversely projected to a net flux through an atmospheric chemistry-transport model. Current methods to partition net fluxes to underlying sector-based emissions often scale fluxes based on the relative weight of sectors in a prior inventory. However, this approach imposes correlation between emission sectors which may not exist. Here we present a Bayesian optimal estimation method that projects inverse methane fluxes directly to emission sectors while accounting uncertainty structure and spatial resolution of prior fluxes and emissions. We apply this method to satellite-derived fluxes over the U.S. and at higher resolution over the Permian Basin to demonstrate that we can characterize a sector-based emission budget. This approach provides more robust comparisons between different top-down estimates, critical for assessing the efficacy of policies intended to reduce emissions.