The Permian Basin has become the United States’ largest producer of oil over the past decade. Along with the rise in production, there has been an increase in the rate of low magnitude earthquakes, some of which have been associated with hydrocarbon extraction and wastewater injection. A detailed knowledge of changes to the subsurface can aid in understanding the causes of seismicity, and these changes can be inferred from InSAR surface deformation measurements. In this study, we show that both cm-level cumulative deformation, as well as mm-level coseismic deformation signals, are detectable in West Texas. In a region west of Mentone, TX, we reconstructed the subtle coseismic deformation signal on the order of ~5 mm associated with the recent M4.9 earthquake. Over ~100,000 km2 of the Permian Basin, we created annual cumulative LOS deformation maps, decomposing into vertical and eastward components where overlapping data are available. These maps contain numerous subsidence and uplift features near active production and disposal wells. The most important deformation signatures are linear streaks that extend tens of kilometers near Pecos, TX, where a cluster of increased seismic events was cataloged by TexNet. As validated by independent GPS data, our InSAR processing strategy achieved millimeter-level accuracy. A careful treatment of the InSAR tropospheric noise, which can be as large as 15 cm in West Texas, is required to detect surface deformation signals with such low signal-to-noise ratio. We developed an outlier removal technique based on robust statistics to detect the presence of strong, non-Gaussian noise. We compared the surface deformation solutions of multiple InSAR time series methods, and all of them produced more accurate and consistent deformation trends after removing outlier InSAR measurements. We are exploring a Bayesian generalization of SBAS velocity estimation by including probabilistic data rejection to determine which pixels should be excluded from the model fitting. This technique provides a full posterior distribution of the model parameters along with the best-fit surface velocity.