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copied!<p>I made this a new answer since it's fundamentally different.</p> <p>This is based on Chris Bishop, Machine Learning and Pattern Recognition, Chapter 2 "Probability Distributions" p71++ and <a href="http://en.wikipedia.org/wiki/Beta_distribution" rel="nofollow noreferrer">http://en.wikipedia.org/wiki/Beta_distribution</a>.</p> <p>First we fit a beta distribution to the given mean and variance in order to build a distribution over the parametes. Then we return the mode of the distribution which is the expected parameter for a bernoulli variable.</p> <pre><code>def estimate(prior_mean, prior_variance, clicks, views): c = ((prior_mean * (1 - prior_mean)) / prior_variance - 1) a = prior_mean * c b = (1 - prior_mean) * c return ((a + clicks) - 1) / (a + b + views - 2) </code></pre> <p>However, I am quite positive that the prior mean/variance will not work for you since you throw away information about how many samples you have and how good your prior thus is. </p> <p>Instead: Given a set of (webpage, link_clicked) pairs, you can calculate the number of pages a specific link was clicked on. Let that be m. Let the amount of times that link was not clicked be l. </p> <p>Now let a be the number of clicks to your new link be a and the number of visits to the site be b. Then your probability of your new link is</p> <pre><code>def estimate(m, l, a, b): (m + a) / (m + l + a + b) </code></pre> <p>Which looks pretty trivial but actually has a valid probabilistic foundation. From the implementation perspective, you can keep m and l globally.</p>

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