Catalogue of Artificial Intelligence Techniques

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Bayesian Inference

Aliases: Statistical Inference

Keywords: cycle cutset, hugin, tree clustering

Categories: Inference and Reasoning

Author(s): Robert Corlett , Judea Pearl

Bayesian inference is one means by which knowledge based systems can reason when uncertainty is involved. Given a set of mutually exclusive hypotheses ${H}_{i}^{}$ and an evidence event $E$, we obtain from an expert estimates of the prior probabilities $P\left({H}_{i}^{}\right)$, and the conditional probabilities $P\left(E|{H}_{i}^{}\right)$. Bayes' Rule then gives the probability of ${H}_{i}^{}$ given evidence $E$:

$P\left({H}_{i}^{}|E\right)=c\cdot P\left(E|{H}_{i}^{}\right)\cdot P\left(H\right)$

where $c$ is a normalising constant ensuring that $P\left({H}_{i}^{}|E\right)$ sum to unity. In practical problems $E$ may be any subset of the set of all possible evidence events and the hypothesis of interest may be any subset of the set of all possible hypotheses. This tends to require a vast number of conditional probabilities to be calculated. A solution is provided by techniques based on Bayesian Networks. To specify such a network one need only estimate the conditional probabilities of each elementary event ${E}_{j}^{}$ given its immediate causes. When the network formed by these cause-effect relationships is loop free, the probability $P\left(H|E\right)$ for any subset $E$ of evidence events and any subset $H$ of hypotheses can be calculated by distributed message-passing techniques. When cycles are unavoidable, tree clustering and cycle cutset techniques (see Constraint Networks) can be used to compute $P\left(H|E\right)$. An example of the use of Bayesian inference is the HUGIN system.

References:

• Andersen, S.K., Olesen, K.G., Jensen, F.V. and Jensen, F., Hugin--a shell for building Bayesian belief universes for expert systems. Proceedings of IJCAI-89, 1080--1085.
• Pearl, J., Probabilistic Reasoning in Intelligent Systems: networks of plausible inference , Morgan Kaufmann, San Mateo, California, 1988.