The spatial structure of the subsurface is an important factor when interpreting seismic data. The Bayesian methodology is a valuable tool for integrating these spatial relations in the inversion process as it merges the information together and assesses the uncertainty of the model. In the everyday use of the Bayesian methodology, however, the computational cost is a challenge. We describe a new approach that utilizes a local neighborhood to include the spatial constraints and assess the uncertainties in the inversion using fast and parallelizable computations. The approach is applicable for both discrete lithology-fluid prediction and estimation of rock properties, such as porosity and saturation.