Bayes Estimator - Practical Example of Bayes Estimators

Practical Example of Bayes Estimators

The Internet Movie Database has used a formula for calculating and comparing the ratings of films by its users, including their Top Rated 250 Titles which is claimed to give "a true Bayesian estimate":

where:

= weighted rating

= average for the movie as a number from 0 to 10 (mean) = (Rating)

= number of votes for the movie = (votes)

= minimum votes required to be listed in the Top 250 (currently 25000)

= the mean vote across the whole report (currently 7.1)

As the number of ratings surpasses "m", the weighted bayesian rating (W) approaches a straight average (R). The closer "v" (the number of ratings for the film) is to zero, the closer "W" gets to "C", where W is the weighted rating and C is the average rating of all films. So, in simpler terms, films with very few ratings/votes will have a rating weighted towards the average across all films, while films with many ratings/votes will have a rating weighted towards its average rating. IMDB's use of Bayesian estimates ensures that a film with only a few hundred ratings, all at 10, would not rank above "the Godfather", for example, with a 9.2 average from over 500,000 ratings. The fewer ratings/votes a film has, the closer its weighted "bayesian" rating is to the mean rating of all films on IMDB, while the more votes/ratings a film gets, the closer its weighted "bayesian" rating gets to the pure average/mean for that individual film.