Posterior variance in conjugate models | Poisson-gamma
14 hours ago
- Posterior variance can increase under the beta-binomial model when unexpected data occurs, though precision always improves.
- In the normal-normal model, precision (reciprocal of variance) increases with each new data point, consistently reducing posterior variance.
- For the Poisson-gamma model, posterior variance rises with each observed event (k) and decreases quadratically with time (t) between events.
- An illustration using simulated Poisson data with a gamma(1,1) prior demonstrates how posterior variance behaves over time.