Amazon Rankings

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. \(R = \frac{1}{N} \sum_{i} n_i r_i \)

Then, the Bayesian rating \(\tilde{r_i}\) is: