The detection and quantification of methane and other trace gases emissions using remote sensing with imaging spectroscopy is an increasingly important tool for understanding local, regional, and global emissions. Traditional algorithms for quantifying the emission rate often rely on user-determined, instrument-dependent parameters and arbitrary plume boundaries. In this paper we present a new algorithm to estimate the emission rate based on a statistical inversion of a physical plume model that does not depend on such parameter choices or plume boundaries, termed SPIIRE. The method fully exploits instrument noise models, incorporates surface-albedo and atmospheric effects present in gas enhancement imagery, and is well suited for operational use. We present simulation results showing improved noise resilience, demonstrate performance against controlled-release experimental data using AVIRIS-3 and EMIT, and provide multiple examples using EMIT. We then show how the model can be extended to complex scenes having overlapping plumes and to spatially-distributed sources like landfills.