# Derivation of Bayes classifier equation

by Francesco Boi   Last Updated September 11, 2019 09:19 AM

In the Elements of Statistical learning book when introducing Linear Discriminant Analysis it says:

A simple application of Bayes theorem gives us

$$Pr(G=K|X=x) = \frac{f_k(x)\pi_k}{\sum_{l=1}^Kf_l(x)\pi_l}$$

where $$\pi_k$$ is the prior probability of class $$k$$ and $$f_k(x)$$ is the class conditional probability.

1. What is the class conditional probability? Is it $$Pr(X=x|G=K)$$?
2. How is derived the above equation from the Bayes theorem? I know $$Pr(G=K|X=x) = \frac{Pr(X=x|G=K)Pr(G=K)}{Pr(X=x)}$$

I know that $$Pr(G=K)=\pi_k$$ but I do not know how to derive the rest of the equation.

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