Bayesian updating: Binomial likelihood with Beta prior

This demo illustrates how the posterior distribution and its mean and variance evolve with additional observed coin tosses. This demo was created by Adarsh Pyarelal with assistance from Claude on 2026-03-23.

Beta prior $$p(r \mid a, b) = \mathrm{Beta}(r | a, b)$$

Parameter $a$

Parameter $b$

Observations

Posterior mean

0.50

Posterior variance

0.083

Toss sequence

No tosses yet

After latest toss (0 H, 0 T)

Posterior mean over tosses

Posterior variance over tosses