Figure 3: Probability estimates and inferences for the Dirichlet -Poisson -Binomial with each α$_{i}$ = 1 /k . The 20 genes with the largest tag counts are arranged in decreasing rank order along the X-axis. The observed tag proportions are marked in dark circles, the standard MLE in dark triangles. In this case analytically derived posterior modes deviate substantially from MLE. However, estimated posterior mean is identical to MLE in this case. Upper and lower 95% Bayesian Credible bounds are also given. 33 Gene Index: Decreasing Rank Estimates 0 5 10 15 20 0.00 0.01 0.02 0.03 0.04 Observed MLE, Post.Mean Post. Mode Lower 95% Cred. Set Upper 95% Cred. Set