prior & posterial

• $theta$ parameters of distribution
• $X$ data R.V
• $P(theta)$ Prior, Prior distribution when not seeing data
• $P(theta | X)$ posterior distribution when seen data
• $P(X | theta)$ Likelihood
• $P(X)$ data distribution

$$P(theta | X) = frac{P(theta)P(X|theta)}{P(X)}$$ $$P(X) = int_theta P(X|theta)P(theta)d theta$$