Gamma–Poisson rate update
Combine event counts and exposure with a shape–rate gamma prior.
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Use shape at least 0.1 and rate greater than zero, a nonnegative integer event count and positive exposure. Use the same exposure unit in the prior rate and observed exposure.
The starting values are hypothetical. Results update as you edit. Use aggregate or synthetic inputs only.
Calculation results
- Posterior shape
- 6
- Posterior rate parameter
- 30
- Posterior mean per exposure unit
- 0.2
- Posterior SD
- 0.081649658
- 95% credible lower
- 0.073396475
- 95% credible upper
- 0.3889444
How to interpret the output
The posterior shape is prior shape plus events; its rate is prior rate plus exposure. Shape divided by rate is the posterior mean event rate per exposure unit. A homogeneous Poisson process and specified prior are assumed; overdispersion, clustering and changing rates are not modeled.
Method referenceSource checked 2026-11-06. Read the reproducible calculator validation report.