Here is the rating summary of a product,
Good – 40%
Average – 10%
Poor – 50%
Looking at the product, how do you know which view represents the actual quality of the product?
Can we conclude that the probability of the product being good equals 0.4, average 0.1, and poor 0.5? Although that is what we want from the rating system, we must realise that these may not represent the absolute or marginal probability of quality but the conditional probability, e.g., the probability of good a given person has rated. In other words
P(Good|Rated) = 0.4
P(Average|Rated) = 0.1
P(Poor|Rated) = 0.5
From this information, we can estimate the actual probabilities, P(Good), P(Average) and P(Poor) using Bayes’ theorem.
P(Good|Rated) = P(Rated|Good) x P(Good) / P(Rated)
P(Average|Rated) = P(Rated|Average) x P(Average) / P(Rated)
P(Poor|Rated) = P(Rated|Poor) x P(Poor) / P(Rated)
