Bayes factor for Poisson rate test and posterior distribution characterization for Poisson inference

To estimate the Bayes factor, it is assumed that the mean parameter of interest is sampled from Gamma(300,3) and Gamma(200,2) under the null and alternative hypothesis, respectively. The Bayes factor that is estimated by the procedure is 1.121, which means that the observed data gives weak evidence in favor of the null distribution.

To compute the posterior distribution, the Jeffreys prior is used by specifying the parameter of interest follows Gamma(0.5,1). The estimated posterior mode and mean are both 95.66. Given the observed data, the credible interval (94.78, 96.54) gives the area that has a 95% Bayesian coverage for the mean of the previous experiences. The posterior distribution plot illustrates the entire information about the mean of interest given the observed data.