efficiently predicting the likelihood of a user clicking a hyperlink

Question

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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.

Answer 1

I hate to give a non-answer here, but doesn't the likelihood that your user click the link depend on the type of link it is? Or is this ads of some sort? Even then, it would be content-dependent, wouldn't it? I would be tempted to say this is more of a psychology question than a statistics one... ;]