Zhe Li

Bayes’ Formula and Updating Probability Estimates

Bayes’ Formula is a rational method for adjusting our viewpoints as we confront new information.

Bayes’ formula makes use of the total probability rule:

P(A)=\sum_nP(A\cap B_n)

\text{Updated probability of event given the new information} = \frac{\text{Probability of the new information given event}}{\text{Unconditional probability of the new information}}\times \text{Prior probability of event}

In probability notation, this formula can be written concisely as follows:

P(Event|Information)=\frac{P(Information|Event)}{P(Information)}P(Event)