Quantifying methane (CH4) emissions from the oil and natural gas (O/NG) production sector is an important regulatory challenge in the United States. In this study, we conduct a set of inversion calculations using different methods to quantify lognormal distributed CH4 surface fluxes in the Haynesville-Bossier O/NG production basin in Texas and Louisiana, combining three statistical cost functions, four meteorological configurations, and two days of aircraft measurements from a 2013 field campaign. We aggregate our posterior flux estimates to derive our best estimate of the basin-wide CH4 emissions, 76 metric tons/hr, with a 95% highest density interval of 51–104 metric tons/hr, in agreement with previous estimates using mass balance and eddy covariance approaches with the same aircraft measurements. Our inversion estimate of basin-wide CH4 emissions is 133% (89%–182%, 95% highest density interval) of a gridded Environmental Protection Agency's inventory for 2012, and the largest discrepancies between our study and this inventory are located in the northeastern quadrant of the basin containing active unconventional O/NG wells. Our inversion approach provides a new spatiotemporal characterization of CH4 emissions in this O/NG production region and shows the usefulness of inverse modeling for improving O/NG CH4 emission estimates. ©2019. The Authors.