A Bayesian average is a method of estimating the mean of a population where instead of estimating the mean strictly from the available data set, other information – especially a pre-existing belief with regard to the population which is a central feature of Bayesian interpretation – is incorporated into the calculation which is especially relevant when the available data set is small.
Bayesian average is in widespread use ranging from marketing to genetics.
Calculating the Bayesian average uses the prior mean m and a constant C. C is assigned a value that is proportional to the typical data set size. The value is larger when the expected variation between data sets (within the larger population) is small. It is smaller when the data sets are expected to vary substantially from one another.
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