We have developed a probabilistic formulation to derive the probability density function of amplitude variation with offset (AVO) attributes given the distribution of elastic properties, in the context of AVO analysis of well log data. The proposed probabilistic formulation includes the analytical expression of the posterior distribution and contributes to the correct propagation of the uncertainty through the AVO model. When this analysis is performed in each facies, the resulting posterior probability density functions of AVO attributes, conditioned by the elastic attributes and the underlying log-facies classification, can be used in a Bayesian inversion workflow to obtain the AVO-attribute-based facies classification. This classification is then compared with the petrophysical log-facies profile and can be extended to the entire reservoir model if inverted seismic attributes are available. We demonstrate the methodology on a data set from an onshore tight-sand gas reservoir in Texas. The main results of the application are the set of probability distributions of AVO properties as a function of elastic attributes in each facies and the corresponding AVO-based facies profile at the well location. A comparison of different statistical assumptions and a sensitivity analysis on the resolution of the elastic data set are presented.