= Poisson mean equality model comparison
Compare independent Poisson means with one shared mean under proper shape-rate <gamma distribution> priors. Adding the second mean as an inactive parameter under the shared-mean model gives a simple identity model switch. With equal model priors and identical active/inactive priors, its ratio from separate to shared means is $e^{\gamma_2-\gamma_1}(\gamma_1/\gamma_2)^{x_2}$. <Poisson-gamma conjugacy> supplies exact within-model updates, and integrating the gamma kernels supplies an independent <Bayes factor> benchmark.
Back to article page
