Bayesian Approach to Classification

The Bayesian approach is an indirect method for classification that models probabilities to determine class membership. It involves three main steps:

1. Model the class-conditional likelihood for each class,

   $$p\left(x\mid C_k\right).$$

2. Model the prior probability for each class,

   $$p\left(C_k\right).$$

3. Use Bayes’ formula to calculate the posterior probability, $p\left(C_k\mid x\right)$, which is the probability of a class given the input data.

The Bayesian Formula is:

$$p\left(C_k\mid x\right)=\frac{p\left(x\mid C_k\right)p\left(C_k\right)}{p(x)}$$

Here, $p(x)$ is the “evidence” and acts as a scaling factor that does not influence the classification decision.