GT: Bayes' rule

Bayes' Rule Explained

Introduction to Bayes' Rule

• The lecture introduces Bayes' Rule, focusing on understanding the relationship between two events, K and L.

• It poses a question about determining the probability of event K given that event L has occurred.

Deriving Bayes' Rule

• Bayes' Rule states: P(K|L) = P(L|K) * P(K) / P(L), where:

• P(K|L): Probability of K given L.

• P(L|K): Probability of L given K.

• P(K): Probability of K.

• P(L): Probability of L.

Visual Representation

• A visual representation is used to explain the concept:

• The entire circle represents the probability mass of event L (P(L)).

• The intersection area represents the joint probability of both events occurring (P(K ∩ L)).

Rearranging Probabilities

• By rearranging terms, we can express joint probabilities in different forms:

• From conditional probabilities: P(K ∩ L) = P(K|L) * P(L).

Final Formulation

• Combining expressions leads to the final formulation of Bayes’ Rule:

• This shows how to calculate the probability of one event based on another's occurrence, emphasizing its practical application in statistical reasoning.