I'm looking for a rating system that does not only weight the rating on number of votes, but also time and "activity"
To clarify a bit:
Consider a site where users produce something, like a picture. There is another type of user that can vote on other peoples pictures (on a scale 1-5), but one picture will only recieve one vote.
The rating a productive user gets is derived from the rating his/hers pictures have recieved, but should be affected by:
A user who's getting 3's and 4's and still making 10 pictures per week should get higher rating than a person that have gotten 5's but only made 1 pic per week and stopped a few month ago.
I've been looking at Bayesian estimate, but that only considers the total amount of votes independent of time or productivity.
My math fu is pretty strong, so all I need is a nudge in right direction and I can probably modify something to fit my needs.
There are many things you could do here.
The obvious approach is to have your measure of the scores decay with time in your internal calculations, for example using an exponential decay with a time constant T. For example, use value = initial_score*exp(-t/T) where t is the time that's passed since picture was submitted. So if T is one month, after one month this score will contribute 1/e, or about 0.37 that it originally did. (You can also do this differentially, btw, with value -= (dt/T)*value, if that's more convenient.)
There's probably a way to work this with a Bayesian approach, but it seems forced to me. Bayesian approaches are generally about predicting something new based on a (usually large) set of prior data, which doesn't directly match your model.