Bayesian Classification:

• Bayesian classifiers are statistical classifiers.

• They can predict class membership probabilities, such as the probability that a given tuple belongs to a particular class.

• Each Bayesian example can incrementally increase or decrease the probability that a hypothesis is correct-prior knowledge can be combined with observed data.

• Bayesian classification is based on Bayesian theorem.

• Bayesian classifiers have also exhibited high accuracy and speed when applied to large databases.

Naïve Bayesian classifiers:

• These assume that the effect of an attribute value on a given class is independent of the values of the other attributes.

• This assumption is called class conditional independence.

• It is made to simplify the computations involved in this.

Bayesian Theorem:

• The purpose of Bayesian theorem is to predict the class label for a given tuple.

• Let X be a data tuple.

• In Bayesian terms, X is considered “evidence.”

• it is described by measurements made on a set of n attributes.

• Let H be some hypothesis, such as that the data tuple X belongs to a specified class C.

• For classification problems, we are looking for the probability that tuple X belongs to class C, given that we know the attribute description of X.