This paper proposes a Bayesian approach to perform inference in the exact affine Stone index (EASI) demand system that was proposed by Lewbel and Pendakur (2009), while taking into account nonlinearity and endogeneity. A Bayesian approach enables us to easily handle censored data, test and impose inequality restrictions (strict cost monotonicity) and concavity of the cost function, and perform inference of nonlinear functions of the parameter estimates as by-product of the posterior chains. We compare our proposal with Lewbel and Pendakur (2009)'s results, based on iterative linear three-stage least squares (3SLS). Although we found no statistically significant differences in point estimates between these two approaches, it seems that ignoring censoring overestimates precision.