Sampling Based Approach for Combining Results from Binomial Experiments

In this paper, the problem of information related to I binomial experiments, each having a distinct probability of success ${\theta}_i$, i = 1,2, $\cdots$, I, is considered. Instead of using a standard exchangeable prior for ${\theta}\;=\;({\theta}_1,\;{\theta}_2,\;{\cdots},\;{\theta}_I)$, we con-sider a partition of the experiments and take the ${\theta}_i$'s belonging to the same partition subset to be exchangeable and the ${\theta}_i$'s belonging to distinct subsets to be independent. And we perform Gibbs sampler approach for Bayesian inference on $\theta$ conditional on a partition. Also we illustrate the methodology with a real data.