Similarly, it can be shown that the marginal distribution of i ) for ∈ {a, b}.
the integrand above is proportional to the beta-binomial distribution with number of trials N a k + N b k , successes x + y, and parameters β o and ( Then expression (1) above becomes: We cannot observe N a kb , N b kn , N a k and N b k explicitly, but we can estimate them by obtaining posterior samples from our Gibbs sampler.