Basic Bayesian Statistics

Prior Probability

Basically a probability of seeing an outcome → normal probability.

• $\text{Error}=\min \{P({\omega }_1),P({\omega }_2)\}$
• Intuition is to make the decision with minimal error probability.

Posterior Probability

The probability of the cause given the results.

• $\text{Error}=\min \{P({\omega }_1|x),P({\omega }_2|x)\}$
• Also minimize the error. Calculating the posterior $P({\omega }_i|x)$.

$$P({\omega }_i|x)=\frac{p(x,{\omega }_i)}{p(x)}=\frac{p(x|{\omega }_i)P({\omega }_i)}{p(x)}$$