Shrinkage
Pulling estimates from small samples toward an overall average, so a 2-for-2 record doesn't outrank a 470-for-500 one.
The posterior always lands between the prior's rate and the raw rate, closer to whichever has more visits behind it. That's the whole behavior in one sentence, and it's why this is called shrinkage: noisy estimates are shrunk toward a sensible center, more when they're noisier.
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
- 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.
- credible interval: A range that holds the true rate with a stated probability, according to the posterior. The Bayesian cousin of a confidence interval.
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