I'm not even sure if what I want to do is a good idea but I figure I'll experiment and see.


I have two predicted ratings in the range of 1-5 based on two different algorithms for predicting movie ratings. I also have two global averages for the given movie and given user.


e.g.


predicted rating 1 = 4.5
predicted rating 2 = 2.5


global mean movie = 3.8
global mean user = 3.6


The two most important values here that should for now be equally weighed is the predicted ratings but I want to have to tend towards the global means a bit as well if that makes any sense. 


What mathematical weight average function can I use and how?


This is all experimental so please tell me if you think i'm way off and you have any other ideas. :) My maths is quite rusty.



weighted to centre mean
Possibly what you're looking for is an [empirical Bayes method](http://en.wikipedia.org/wiki/Empirical_Bayes_method).


Here's a bit more on empirical Bayes methods: <http://dspace.mit.edu/bitstream/handle/1721.1/45587/18-441Spring-2002/NR/rdonlyres/Mathematics/18-441Statistical-InferenceSpring2002/0636681D-CFBE-4A76-BC80-D02BB2C2BFB2/0/attachment3.pdf>


I suspect you'd have to say more than you wrote above before much more could be said here.


