22.03.29 - Bayes Rule and Uncertainties

Knowledge Based Systems

To consider decisions we must introduce methods that can cope with uncertainty

Probability

Basic statistical methods deal with uncertainty via probability

Probability = (number of desired outcomes)/ (total number of outcomes)

Bayes Rule

The fundamental notion of Bayesian Statistics is that of conditional probability $P(H|E)$ The probability of a Hypothesis (H) being true based on evidence (E)

$P(H|E)=\frac{P(E|H)*P(H)}{P(E)}$

• $P(H|E)$ - Probability that hypothesis is true given evidence
• $P(E|H)$ - Probability that we will observe evidence given that hypothesis is true
• $P(H)$ - That a priori probability that hypothesis is true in the absence of any specific evidence
• $P(E)$ - Probability of observing E in the absence of any specific hypothesis