Bayesian Statistics¶

• Based on the Bayesian interpretation of probability
• Probability expresses a degree of belief in an event.
• The degree of belief may be based on prior knowledge about the event, such as the results of previous experiments, or on personal beliefs about the event.
• use Bayes' theorem to compute and update probabilities after obtaining new data

Bayes' theorem¶

Stated mathematically as below,

\({P(A\vert B)={\frac {P(B\vert A)P(A)}{P(B)}}}\)

\(P(A\vert B)\)

The probability of event \(A\) occurring given that \(B\) is true.

Conditional probability

Posterior probability of \(A\) given \(B\)

\(P(B\vert A)\)

The probability of event \(B\) occurring given that \(A\) is true.

\(likelihood\) of \(A\) given a fixed \(B\) because \(P(B|A)=L(A|B)\)

\(P(A)\) and \(P(B)\)

The probabilities of observing A and B respectively without any given conditions Prior Probability / Marginal Probability