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Determining the probability of a user clicking a hyperlink
So I have a bunch of hyperlinks on a web page. From past observation I know the probabilities that a user will click on each of these hyperlinks. I can therefore calculate the mean and standard deviation of these probabilities.
I now add a new hyperlink to this page. After a short amount of testing I find that of the 20 users that see this hyperlink, 5 click on it.
Taking into account the known mean and standard deviation of the click-through probabilities on other hyperlinks (this forms a "prior expectation"), how can I efficiently estimate the probability of a user clicking on the new hyperlink?
A naive solution would be to ignore the other probabilities, in which case my estimate is just 5/20 or 0.25 - however this means we are throwing away relevant information, namely our prior expectation of what the click-through probability is.
So I'm looking for a function that looks something like this:
double estimate(double priorMean, double priorStandardDeviation, int clicks, int views);
I'd ask that, since I'm more familiar with code than mathematical notation, that any answers use code or pseudocode in preference to math.