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.
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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.