Imagine we have 800 sessions on a landing page and 65 conversions. The raw rate is 65/800 ≈ 8.1%. It looks like a precise number, but is it really? Is it the true conversion probability of the page, or could it be different? And if someone claimed the page converts at least 10% — do the data confirm or contradict that?
Questions like this are everyday fare for anyone working with traffic and conversion data. Bayesian statistics offers an elegant and direct tool to answer them: the Beta distribution.
The Beta distribution is a continuous probability distribution defined on the interval [0, 1]. That sounds abstract, but it’s exactly what we need whenever we want to model the uncertainty around a proportion: a conversion rate, a CTR, a click percentage, a probability of success. Intuitively, Beta is a distribution over the possible probabilities of the event, and that is what makes it unique.
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