We present an analysis of methane (CH4) emissions using atmospheric observations from 13 sites in California during June 2013 to May 2014. A hierarchical Bayesian inversion method is used to estimate CH4 emissions for spatial regions (0.3 degrees pixels for major regions) by comparing measured CH4 mixing ratios with transport model (Weather Research and Forecasting and Stochastic Time-Inverted Lagrangian Transport) predictions based on seasonally varying California-specific CH4 prior emission models. The transport model is assessed using a combination of meteorological and carbon monoxide (CO) measurements coupled with the gridded California Air Resources Board (CARB) CO emission inventory. The hierarchical Bayesian inversion suggests that state annual anthropogenic CH4 emissions are 2.42 +/- 0.49 Tg CH4/yr (at 95% confidence), higher (1.2-1.8 times) than the current CARB inventory (1.64 Tg CH4/yr in 2013). It should be noted that undiagnosed sources of errors or uncaptured errors in the model-measurement mismatch covariance may increase these uncertainty bounds beyond that indicated here. The CH4 emissions from the Central Valley and urban regions (San Francisco Bay and South Coast Air Basins) account for similar to 58% and 26% of the total posterior emissions, respectively. This study suggests that the livestock sector is likely the major contributor to the state total CH4 emissions, in agreement with CARB's inventory. Attribution to source sectors for subregions of California using additional trace gas species would further improve the quantification of California's CH4 emissions and mitigation efforts toward the California Global Warming Solutions Act of 2006 (Assembly Bill 32).