Sequential coherence
Proposition taught in The Beta–Binomial model, part of Bayesian statistics
Sequential coherence
| Type | Proposition |
| Taught in | The Beta–Binomial model |
| Part | Bayesian statistics |
Sequential updating is exact. If data arrive in batches (x_1,n_1) and (x_2,n_2), then \begin{align*} \theta\mid x_1 &\sim\operatorname{Beta}(\alpha+x_1,\beta+n_1-x_1),\\ \theta\mid x_1,x_2 &\sim\operatorname{Beta}(\alpha+x_1+x_2, \beta+n_1+n_2-x_1-x_2), \end{align*} which is the same posterior obtained by combining both batches first.
Used in
- Taught in The Beta–Binomial model, where the derivation and examples are.
- All 11 questions on The Beta–Binomial model
See also
Beta distribution · Beta–Binomial conjugacy · Two pseudo-count conventions · Conjugacy is optional · Beta–Binomial posterior prediction