Beta distribution
A distribution over rates between 0 and 1, set by two counts: think of them as successes and failures seen so far, real or pretend.
The posterior is more than one number. It's a whole spread of plausible rates, a Beta distribution named by two counts: α = prior sales + sales and β = prior non-sales + non-sales. Its mean is α / (α + β), the estimate you've been computing, and its width says how sure you can be.
Try it now
The prior acts like visits you've already seen. A big prior needs lots of data to move; a small one moves quickly.
Learn it properly
Bayesian rates: trusting small numbers · Priors as pseudo-counts, Beta posteriors, shrinkage for small samples, and which of two rates is really higher. About 25 minutes.
Other terms from the same lesson
- credible interval: A range that holds the true rate with a stated probability, according to the posterior. The Bayesian cousin of a confidence interval.
- shrinkage: Pulling estimates from small samples toward an overall average, so a 2-for-2 record doesn't outrank a 470-for-500 one.
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