A prior meets the likelihood and the posterior emerges between them.
From the chapter: Chapter 4: Probability
Glossary: bayes theorem, posterior, prior, likelihood, conjugate prior
People: thomas bayes, pierre simon laplace
Transcript
Bayesian inference is a recipe for updating a belief when new data arrives.
The starting belief is the prior. Here, a wide normal distribution centred at zero. It captures what is believed before any data is seen.
A measurement comes in, with mean two. The likelihood, in red, shows how plausible each possible value of the parameter is, given that observation.
Multiplying prior by likelihood and normalising gives the posterior in blue. It sits between prior and likelihood, weighted by the precision of each.
When the sample size grows, the likelihood narrows. The data become more certain, so the posterior shifts toward them.
With thirty samples the prior barely matters. The posterior collapses onto the maximum-likelihood estimate.
Tighten the prior instead, and even thirty samples cannot move it much. Strong priors resist the data.
That is the entire mechanism. Three quantities, one rule, and a way to keep beliefs honest as evidence accumulates.