Bayesian inference (original) (raw)

Bayesian inference is statistical inference in which probabilities are interpreted not as frequencies or proportions or the like, but rather as degrees of belief. In other words, it attempts to reduce statistical inference to Bayesian probability. Bayesian inference has applications in artificial intelligence and expert systems.

For a worked example of one form of Bayesian inference, see naive Bayesian classification.

In some applications fuzzy logic is an alternative to Bayesian inference. Fuzzy logic and Bayesian inference, however, are mathematically and semantically not compatible: You cannot, in general, understand the degree of truth in fuzzy logic as probability and vice versa.

Applications

Bayesian inference techniques have been a fundamental part of computerized pattern recognition techniques since the late 1950s. There is growing interest in using Bayesian inference to filter spam. For example: Bogofilter, SpamAssassin and Mozilla.

See also:

• Bayesian model comparison
• Occam's Razor
• Minimum description length

External links

• On-line textbook: Information Theory, Inference, and Learning Algorithms, by David MacKay, has many chapters on Bayesian methods, including introductory examples; compelling arguments in favour of Bayesian methods; state-of-the-art Monte Carlo methods, message-passing methods, and variational methods; and examples illustrating the intimate connections between Bayesian inference and data compression.
• Naive Bayesian learning paper
• A Tutorial on Learning With Bayesian Networks