The Art and Science of Machine Intelligence pp 157-185 | Cite as

# Classical Bayesian Theory and Networks

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## Abstract

By their very nature, Bayesian networks (BN) represent cause-effect relationships by their parent-child structure. One can provide an observation of some events and then execute a Bayesian network with this information to ascertain the estimated probabilities of other events. Another significant advantage is that they can make very good estimates in the presence of missing information, which means that they will make the most accurate estimate with whatever information (or knowledge) is available and will provide these results in a computationally efficient manner as well.

This chapter comprises three separate sections. The first develops some of the basic probability concepts on which classical Bayes theory is based. The second develops Bayes theorem and describes several examples using Bayes theorem. The third addresses classical methods for constructing the Bayesian network structure.

## Keywords

Bayes theory Bayes network K2 algorithm Chain rule of conditional probabilities## Abbreviations

- AUC
Area under curve

- BN
Bayesian network

- CH
Cooper Herskovitz

- CI
Conditional independence

- DAG
Directed acyclic graph

- FN
False negative

- FP
False positive

- GA
Genetic algorithm

- K2
Metric by Cooper and Herskovitz

- MI
Machine intelligence

- NPV
Negative predicted value

- ORACLE
GRNN oracle

- PC
Prediction-causal

- PPV
Positive predicted value

- ROC
Receiver operator characteristic

- SVM
Support vector machine

- TN
True negative

- TNR
True negative rate

- TP
True positive

- TPR
True positive rate

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