Recent applications of passive microwave remote sensing techniques to estimate snow water equivalent (SWE) increasingly rely on the comprehension of microwave emission theories, instead of traditional empirical fitting approaches. In this study, an advanced SWE retrieval algorithm based on the Markov Chain Monte Carlo method was developed. This method samples the posterior multiple-layer snow properties according to the likelihood of the brightness temperature (TB) simulation with the actual TB observations. The Microwave Emission Model of Layered Snowpacks with improved Born approximation (MEMLS-IBA) was used as the observation model. Using a globally applicable method to produce prior estimates of snow properties, the retrieval approach is called the Bayesian Algorithm for SWE Estimation with Passive Microwave measurements (BASE-PM), and was applied on 48 snowpits at Sodanlcyla, Finland; Churchill, Canada and Colorado, US. The result shows that the root mean squared (RMS) error of the retrieved SWE is 42.7 mm excluding two outliers, and is 30.8 mm if the outliers as well as six deep snowpits from Colorado are excluded. This accuracy approximately meets the 30-mm requirement of Integrated Global Observing Strategy for shallow snow. The poor performance for the outlier and deep snowpits is explained. Additional experiments using more accurate priors show that SWE retrieval accuracy can be improved with local snowcover knowledge, e.g. if historical snowpit measurements or snow process model simulations are available. (C) 2017 Elsevier Inc. All rights reserved.