1 Bayes Theorem
\[ \begin{align} p(C|X) = \frac{P(X|C)P(C)}{P(X)} \\ \end{align} \]
Where:
- \(P(C|X)\) is the Posterior (Given the data what is the prob of being class C_k)
- \(P(X|C)\) is the Likelihood (How the data is distributed given C)
- \(P(C)\) is the Prior
- \(P(X)\) is the Evidence/ Marginal likelihood
The evidence \(P(X)\) can also be decomposed in:
\[ \begin{align} P(X) &= \sum_{j}{}P(X,C_j)\\ &= \sum_{j}{}P(X|C_j)P(C_j) \\ \end{align} \]