Statistics

Bayesian inference

Bayesian inference starts from a prior belief about a parameter and updates it with each observation into a posterior. This topic watches that update happen and reads credible intervals from the posterior.

A belief curve over the chance of heads p from 0 to 1, area 1: Beta(21, 11), mean 0.6563, standard deviation 0.0827. The flips so far, 30: H H H T T H H H H T H H T H H H H T H T T T H H H T H T H H.

Intermediate · 30 minYou are hereRead

Bayesian updating

Multiply what you believed by how well each possibility explains the data, rescale, and today’s posterior becomes tomorrow’s prior.

Three belief curves over the chance of heads p from 0 to 1 after 1000 flips, 703 heads. Open-minded: Beta(704, 298), mean 0.7026, 95 % credible interval 0.6739 to 0.7305, drawn as a bar under the curves. Doubtful: Beta(705, 305), mean 0.6980, 95 % credible interval 0.6694 to 0.7259, drawn as a bar under the curves. Keen: Beta(711, 299), mean 0.7040, 95 % credible interval 0.6754 to 0.7317, drawn as a bar under the curves.

Intermediate · 30 minYou are hereRead

Priors, posteriors and credible intervals

A beta prior acts like imaginary earlier flips, the posterior mean blends it with the data, and enough data makes different priors agree.

Bayesian inference

Bayesian updating

Priors, posteriors and credible intervals

Where to go next.

Account

Subjects

Site

Look

Lessons on this topic

Bayesian updating

Priors, posteriors and credible intervals