A hypothesis region is not a separate model
Remark taught in Bayesian hypotheses and model comparison, part of Bayesian statistics
A hypothesis region is not a separate model
| Type | Remark |
| Taught in | Bayesian hypotheses and model comparison |
| Part | Bayesian statistics |
Two constructions must not be confused:
If H_0 and H_1 are regions of one parameter space, compute one posterior and integrate it over the regions.
If M_1 and M_2 have different dimensions or parameterisations, each model needs its own parameter prior and marginal likelihood. A continuous prior on the larger space assigns probability zero to a lower-dimensional surface.
The fruit example is the first construction. Independence in the advertising table is the second.
Used in
- Taught in Bayesian hypotheses and model comparison, where the derivation and examples are.
- All 15 questions on Bayesian hypotheses and model comparison
See also
Marginal likelihood and Bayes factor · Posterior hypothesis probability · Bayes action for two hypotheses · Posterior-odds factorisation