A Bayesian average is a method of estimating the mean of a population consistent with Bayesian interpretation, where instead of estimating the mean strictly from any or all available data set, other existing information related to that data set may also be incorporated into the calculation in order to minimize the impact of large deviations, or to assert a default value when the data set is small.
This was relevant to local SEO and reviews management due to the statement by Google relating to how they determine an average star rating.
?Your score is calculated from user ratings and a variety of other signals to ensure that the overall score best reflects the quality of the establishment.?
Many SEO consultants and people who work with programming algorithms feel that the part about a variety of other signals means that Google uses what is called a Bayesian average to look not just at the raw numbers, but incorporating other factors that may cause deviation in the formula.
In early 2017, Google switched from a minimum of five reviews to Google is awarding stars for as little as one review. The also switched to using a more standard arithmetic mean calculation.