# Bayesian average

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[1] 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.[2]

Bayesian average is in widespread use ranging from marketing to genetics.[3]

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.

${\displaystyle {\bar {x}}={Cm+\sum _{i=1}^{n}{x_{i}} \over C+n}}$

## References

1. ^ "Bayesian Average Ratings". www.evanmiller.org. Retrieved 2016-05-21.
2. ^ Masurel, Paul. "Of Bayesian average and star ratings". fulmicoton.com. Retrieved 2016-05-21.
3. ^ Kruschke, John K.; Aguinis, Herman; Joo, Harry (2012-10-01). "The Time Has Come Bayesian Methods for Data Analysis in the Organizational Sciences". Organizational Research Methods. 15 (4): 722–752. doi:10.1177/1094428112457829. ISSN 1094-4281.
• Yang, Xiao; Zhang, Zhaoxin (2013). "Combining Prestige and Relevance Ranking for Personalized Recommendation". Proceedings of the 22nd ACM international conference on information & knowledge management (CIKM): 1877–1880. doi:10.1145/2505515.2507885.