Precision
Topic of Conjugate analysis for normal models, part of Bayesian statistics
Precision
| Type | Topic |
| Taught in | Conjugate analysis for normal models |
| Part | Bayesian statistics |
| Questions using it | 11 |
The reciprocal of a variance, \tau=1/\sigma^2. In normal models precisions add: the posterior precision of a normal mean is the prior precision plus n/\sigma^2, and the posterior mean is the precision-weighted average of the prior mean and the sample mean.
In Conjugate analysis for normal models
The normal prior respects the fact that \mu may be positive or negative. A log-normal prior would impose positivity, while a bounded uniform prior would assign permanent posterior probability zero outside its bounds. The normal prior can be badly centred, but its nonzero tails allow enough data eventually to overcome that error. It is often convenient to work in precisions \sigma^{-2} and \sigma_0^{-2} because independent information then adds.
Used in
- Taught in Conjugate analysis for normal models
- Also used in Hierarchical Bayes
- Questions that use it (11) — An IQ threshold (answer) · Q7 (answer) · Q19 (answer) · Q28 (answer) · Q49 (answer) · Q50 (answer) · Q58 (answer) · Question 1 (answer) · Question 4 (answer) · Question 5 (answer) · C15 (answer)
- All 19 questions on Conjugate analysis for normal models
See also
Variance · Posterior mean · Precision weighting · Effective sample size · Normal–Normal model · A proper approximation to the flat prior · Normal–Normal conjugacy · Inverse-Gamma distribution