Bayes Theorem

Theorem

$$P(A|B)=P(A)\times \frac{P(B|A)}{P(B)}$$

Robust Version

$$P(A_j|B)=\frac{P(B|A_j)P(A_j)}{{\sum }_{i=1}^{n}P(B|A_i)P(A_i)}$$

Single Partition

$$P(A|B)=\frac{P(B|A)P(A)}{P(B|A)P(A)+P(B|A^c)P(A^c)}$$