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| Sep 29, 2017 | » | The Bayes Formula
1 min; updated Sep 17, 2026
The FormulaBy definition… $$ \mathbb{P}(A) = \mathbb{P}(A \cap B) + \mathbb{P}(A \cap B^{c}) $$ From conditional probability … $$ \mathbb{P}(A) = \mathbb{P}(A|B) \ \mathbb{P}(B) + \mathbb{P}(A|B^c) \ \mathbb{P}(B^c) $$ Therefore $$ \mathbb{P}(B|A) = \frac{ \mathbb{P}(B \cap A) }{ \mathbb{P}(A) } $$ $$ = \frac{ \mathbb{P}(A|B) \mathbb{P}(B) }{ \mathbb{P}(A|B) \ \mathbb{P}(B) + \mathbb{P}(A|B^c) \ \mathbb{P}(B^c) } $$ |
| Oct 9, 2017 | » | Bayesian Rating
1 min; updated Mar 12, 2022
Allows us to weight by review population size.
Then, the Bayesian rating \(\tilde{r_i}\) is: ... |
Switching the roles of the events is convenient because in many problems, one of the conditional probabilities is easier to calculate.
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