Translation to another common notation
Remark taught in Exponential families and conjugacy, part of Bayesian statistics
Translation to another common notation
| Type | Remark |
| Taught in | Exponential families and conjugacy |
| Part | Bayesian statistics |
Some books write the same density as
p(x\mid{\boldsymbol{\eta}}) =h(x)\exp\{{\boldsymbol{\eta}}^{\mathsf T}T(x)-A({\boldsymbol{\eta}})\}.
This is only a change of names: {\boldsymbol{\eta}}=c(\theta), h(x)=b(x), and A({\boldsymbol{\eta}})=\log a(\theta). We retain the a(\theta)–b(x)–c(\theta)–T(x) notation from this point onward.
Used in
- Taught in Exponential families and conjugacy, where the derivation and examples are.
- All 18 questions on Exponential families and conjugacy
See also
Statistic and estimator · Sufficient statistic · Fisher–Neyman factorisation · Minimal sufficiency · Complete statistic · Ancillary statistic · Basu’s theorem · Natural exponential family