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A stochastic method is presented for studying attributes with heterogeneous space-time variations under conditions of uncertainty. The method is a synthesis of the generalized spatiotemporal random field theory and the Bayesian maximum entropy mode of reasoning. The result of this conceptual synthesis is a general and versatile method of spatiotemporal data processing and attribute estimation (prediction) that exhibits a number of attractive features, including the following: The method makes no restrictive assumptions concerning the linearity and normality of the attribute estimator (nonlinear estimators and non-Gaussian probability laws are automatically incorporated), it can study attributes with heterogeneous space-time dependence patterns, and it can account for various kinds of knowledge (core and attribute specific). The method is general, and it can be used to study attributes associated with a variety of systems (physical, technical, medical, and social). Insight into the computational implementation and comparative performance of the proposed method is gained by means of numerical experiments and a real-world case study.