A Bayesian average is a method of estimating the mean of a population using outside information, especially a pre-existing belief,[1] which is factored into the calculation.
[2] Calculating the Bayesian average uses the prior mean m and a constant C. C is chosen based on the typical data set size required for a robust estimate of the sample mean.
It is smaller when the data sets are expected to vary substantially from one another.
are binary values 0 or 1, m can be interpreted as the prior estimate of a binomial probability with the Bayesian average giving a posterior estimate for the observed data.
In this case, C can be chosen based on the desired binomial proportion confidence interval for the sample value.