# Bayesian Statistics

 Random Link ¯\_(ツ)_/¯ Oct 9, 2017 » Bayesian Rating 1 min; updated Jan 11, 2022 Allows us to weight by review population size. Let $$n_i$$ be the number of reviews that item $$i$$ gets, and let $$r_i$$ be the naive average rating of item $$i$$ Let $$N$$ be the total number of reviews across brands, i.e. $$N = \sum_{i} n_i$$ Let $$R$$ be the average rating over all items across brands, i.e. $$R = \frac{1}{N} \sum_{i} n_i r_i$$... Jul 26, 2020 » Bayesian Statistics [MIT 18.650] Sep 29, 2017 » The Bayes Formula 1 min; updated Mar 14, 2021 The Formula By 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 $$\mathbb{P}(B|A) = \frac{ \mathbb{P}(B \cap A) }{ \mathbb{P}(A) }$$ $$= \frac{ \mathbb{P}(A|B) \mathbb{P}(B) }{ \mathbb{P}(A|B) \ \mathbb{P}(B) + \mathbb{P}(A|B^c) \ \mathbb{P}(B^c) }$$ Switching the roles of the events is convenient because in many problems, one of the conditional probabilities is easier to calculate....