The statistical inference drawn from the difference between two independent Poisson parameters is often discussed in medical literature. Kawasaki and Miyaoka (2012) proposed an index θ = P(λ1,post < λ2,post), where λ1,post and λ2,post denote Poisson parameters following posterior density. A new calculation method is proposed using MCMC and an approximate expression and exact expression for θ are compared.
Kawasaki, Yohei and Miyaoka, Etsuo
"Comparison of Three Calculation Methods for a Bayesian Inference of Two Poisson Parameters,"
Journal of Modern Applied Statistical Methods:
1, Article 26.
Available at: http://digitalcommons.wayne.edu/jmasm/vol13/iss1/26