An Algebra for Probabilistic Databases

An algebra is presented for a simple probabilistic data model that may be regarded as an extension of the standard relational model. The probabilistic algebra is developed in such a way that (restricted to α -acyclic database schemes) the relational algebra is a homomorphic image of it. Strictly probabilistic results are emphasized. Variations on the basic probabilistic data model are discussed. The algebra is used to explicate a commonly used statistical smoothing procedure and is shown to be potentially very useful for decision support with uncertain information. Index Terms − Bayes and Markov networks, data models, decision support, probability, relational algebra.