# 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.