Figure 5. Probability estimates for the Dirichlet -Multinomial -Binomial model with all 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. 

Figure 6. Probability estimates for the Missing Data Algorithm where all α$_{i}$ = 1. 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. The analytically computed posterior mode α$_{i}$ = 1 coincides exactly with the MLE. Also included are the estimated posterior mean and upper and lower 95% Bayesian Credible bounds based on MCMC sampling. 

Figure 7. Probability estimates for the Missing Data Algorithm where 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. 

