# Bayesian Models

Bayesian uses the concept of prior belief about the parameter of interest. Then the uncertainty of changes according to the data . Here Bayesian interprets as a random variable, and the prior belief is given in the form of probability density of . In a Bayesian model we will investigates the postrior density of .Conditional probability. Let and be two events where . Then the conditional probability of given can be defined as

Law of total probability. Let and be two events. Then we can write the probability as

Bayes rule. Let and be events such that the 's are mutually disjoint, and for all . Then

Concept of Independence. Intuitively we would like to say that and are independent if knowing about one event give us no information about another. That is, and . We say and are independent if

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