What methodologies are commonly used to model the mean of a population member's value for some metric, given the global mean and with a small sample for the population member?For instance, say we're talking about book reviews where the database has 10,000 reviews (with data, so one can compute global variance etc.) with an average of 6/10, and Customer A has given 1 review of 9/10. It would be incorrect to model that Customer A as always giving scores of 9 for some random book; their actual expected rating would likely be much closer to the global mean.But what would a theoretically correct, "best guess" mix of the global average and user average, when trying to model what rating Customer A gives to some random book?

Perhaps it would be better to approach this from the individual book's perspective.For instance a book has 7 ratings, with an average of 8 and variance of 9. And let's say the global variance is 5, global mean 6.So knowing the local and global averages and variances for this book, what's the best guess estimate we can make for future ratings for this book? In other words, for this book's "true" mean rating?I believe a varLocal/varGlobal weighting factor should be somewhere in there, as I would presume that if the local variance is low, the local mean should have a higher weight. So a model would be something like:[EDIT: The equation is wrong, it should be divided by the square root factor not multiplied by, and the factor should be CountGlobal/CountLocal - but I didn't want to redo the Latex ]Which in our instance would be:alpha*(9/5)/sqrt(10000/7)*(6-8) + 8Where alpha is some scalar. Which if alpha is 1, would be 7.905.Does anyone have any suggestions that would be an improvement over this formula?

I suggest you state your -actual- problem, rather than trying to analogize it.regards,

I don't really have an actual problem, this is an in-general question on modeling subset averages incorporating the global population mean, and applies to many things.

Well, give a finance example, then.