Bayesian average

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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.

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.

 \bar{x} = {Cm + \sum_{i=1}^n{x_i} \over C + n}


  • 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. 

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