GammaPosterior
Gammaposterior, commonly referred to as the gamma posterior, is the posterior distribution of a positive rate parameter in Bayesian statistics when the prior distribution is a Gamma distribution. It arises from a conjugate prior relationship: if the data are modeled by a Poisson or Poisson-like likelihood, a Gamma prior yields a Gamma posterior, making analytic updating straightforward.
In the typical Poisson model, suppose N events are observed over an exposure time T, and the
The gamma posterior provides a convenient framework for uncertainty quantification and inference on the rate parameter.
Parameter choice for the prior (α, β) encodes prior beliefs about the rate; larger α and β shift and tighten