In Bayesian inference, some researchers have examined the difference of binominal proportions using θ = P(π1 > π2 − Δ0|X1,X2), where Xi denote binomial random variable with parameter πi. An approximate method and the MCMC method are compared with an exact method for θ, and results of actual clinical trials using θ are presented.
Kawasaki, Yohei; Shimokawa, Asanao; and Miyaoka, Etsuo
"Comparison of Three Calculation Methods for a Bayesian Inference of P(π1 > π2),"
Journal of Modern Applied Statistical Methods:
2, Article 15.
Available at: http://digitalcommons.wayne.edu/jmasm/vol12/iss2/15