Operations Research
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic inference and influence diagrams
Operations Research
Introduction to Bayesian Networks
Introduction to Bayesian Networks
Uncertain Information Processing in Expert Systems
Uncertain Information Processing in Expert Systems
Decomposition of Multidimensional Distributions Represented by Perfect Sequences
Annals of Mathematics and Artificial Intelligence
Probabilistic partial knowledge handling
International Journal of Approximate Reasoning
Compositional models and conditional independence in evidence theory
International Journal of Approximate Reasoning
Marginalization in composed probabilistic models
UAI'00 Proceedings of the Sixteenth conference on Uncertainty in artificial intelligence
Local computations in Dempster--Shafer theory of evidence
International Journal of Approximate Reasoning
Compositional models in valuation-based systems
International Journal of Approximate Reasoning
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Decomposable models and Bayesian networks can be defined as sequences of oligo-dimensional probability measures connected with operators of composition. The preliminary results suggest that the probabilistic models allowing for effective computational procedures are represented by sequences possessing a special property; we shall call them perfect sequences. The present paper lays down the elementary foundation necessary for further study of iterative application of operators of composition. We believe to develop a technique describing several graph models in a unifying way. We are convinced that practically all theoretical results and procedures connected with decomposable models and Bayesian networks can be translated into the terminology introduced in this paper. For example, complexity of computational procedures in these models is closely dependent on possibility to change the ordering of oligo-dimensional measures defining the model. Therefore, in this paper, lot of attention is paid to possibility to change ordering of the operators of composition.