Yeah, that's a lot of jargon associated with Bayesian statistics, but at it's root the idea is simple. How to merge information you have before observing some data (a.k.a. prior) with new information you just observed, to obtain updated information (a.k.a. posterior) that includes both what you believed initially + the new evidence you observed.
The probability machinery (Bayes rule) is a principled way to do this, and in the case of count data (number of positive reviews for the cafe) works out to give be a simple fraction n/(n+x).
Define:
x = parameter of how skeptical you are in general about the quality of cafes (large x very sceptical),
m = number of positive reviews for the cafe,
p = m+1 / (m+1+x) your belief (expressed as a probability) that the cafe is good after hearing m positive reviews about it.
Learning about the binomial and the beta distribution would help you see where the formula comes from. People really like Bayesian machinery, because it has a logical/consistent feel: i.e. rather than coming up with some formula out of thin air, you derive the formula based on general rules about reasoning under uncertainty + updating beliefs.
The probability machinery (Bayes rule) is a principled way to do this, and in the case of count data (number of positive reviews for the cafe) works out to give be a simple fraction n/(n+x).
Define: x = parameter of how skeptical you are in general about the quality of cafes (large x very sceptical), m = number of positive reviews for the cafe,
p = m+1 / (m+1+x) your belief (expressed as a probability) that the cafe is good after hearing m positive reviews about it.
Learning about the binomial and the beta distribution would help you see where the formula comes from. People really like Bayesian machinery, because it has a logical/consistent feel: i.e. rather than coming up with some formula out of thin air, you derive the formula based on general rules about reasoning under uncertainty + updating beliefs.