# Data Mining Bayesian Classifiers

• Bayesian classifiers are statistical classifiers with Bayesian probability understandings. Bayesian classification uses Bayes theorem to predict the occurrence of any event.
• Bayes theorem came into existence after Thomas Bayes, who first utilized conditional probability to provide an algorithm that uses evidence to calculate limits on an unknown parameter.

## Bayes's theorem DataMining Bayesian Classifiers

• Where X and Y are the events and P (Y) ≠ 0
• P(X/Y) is a conditional probability that describes the occurrence of event X is given that Y is true.
• P(Y/X) is a conditional probability that describes the occurrence of event Y is given that X is true.
• P(X) and P(Y) are the probabilities of observing X and Y independently of each other. This is known as the marginal probability.

## Bayesian Interpretation

In the Bayesian interpretation, probability determines a "degree of belief."
For example, Lets us consider an example of the coin. If we toss a coin, then we get either heads or tails, and the percent of occurrence of either heads and tails is 50%. If the coin is flipped numbers of times, and the outcomes are observed, the degree of belief may rise, fall, or remain the same depending on the outcomes.

Proposition X and evidence Y,

• P(X), the prior, is the primary degree of belief in X
• P(X/Y), the posterior is the degree of belief having accounted for Y.
• The quotient P(Y/X) / P(Y) represents the supports Y provides for X.

Bayes theorem can be derived from conditional probability: • Where P (X⋂Y) is the joint probability of both X and Y being true, because ## Bayesian network

• Bayesian Network falls under classification of Probabilistic Graphical Modelling (PGM) that is utilized to compute uncertainties by utilizing the probability concept.
• A Directed Acyclic Graph show a Bayesian Network, like some other statistical graph, a DAG consists of a set of nodes and links, where links signify connection between nodes. Directed Acyclic Graph

• Here nodes represent random variables, and the edges define the relationship between these variables.