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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.

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Possibly what you're looking for is an 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.

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