genes ranked from largest to smallest. Behavior and trends are almost identical to the DPB model. For the case where all α$_{i}$ = 1, the posterior mean was systematically smaller than the posterior-mode/MLE for cases with large tag counts. The posterior-mode was distinctly different than the unadjusted tag proportions and both sets were above the upper credible bounds for the posterior mean. In the case where all α$_{i}$ = 1 /k , the posterior-mean again matches the corrected MLE almost exactly. The posterior mode tracks the mean closely but is always larger and the unadjusted proportions are usually outside the credible region. Instead of renormalizing the probabilities θ$_{i}$ = ( m$_{i}$φ$_{i}$ ) / ( $^{∑}$m$_{i}$ φ$_{i}$ ) and doing inference based on the posterior of eq. (5), a second more straightforward approach uses missing data. Considering again a data generation process as described in section 3.2, we augment the observed data vector T with an extra category which represents any cDNA that is not converted to a SAGE tag. This count is not observed, but if a distribution such as a Poisson is proposed, we may consider a Bayesian approach. The resulting posterior distribution for the data is, where we have assumed a Dirichlet prior on the unknown initial proportions m ∼ D$_{k}$( α$_{1}$, . . . , α$_{k}$ ) . The resulting posterior distribution is a Dirichlet distribution with k + 1 categories, com- pared with the k categories in the initial distribution m . In particular the distribution is a D$_{k}$$_{+1}$( t$_{1}$ + α$_{1}$, . . . , t$_{k}$ + α$_{k}$, r + 1). By integrating over the missing data term or otherwise eliminating it, it is possible to sample from the joint distribution whose success probability is m$_{i}$φ$_{i}$ . According to the marginalization property of the Dirichlet (Bilodeau & Brenner, 1999) the distribution of any subset of variables ( θ$_{i}$$_{1}$, θ$_{i}$$_{2}$, . . . , θ$_{i}$$_{j}$ ) from a D$_{k}$( α$_{1}$, α$_{2}$, . . . , α$_{k}$ ) with $^{∑}$α$_{i}$ = p is distributed 4.3 A Missing Data Approach. [ m | T , α ] ∝ (1 − k ∑ i =1 m$_{i}$φ$_{i}$ ) r k ∏ i =1 ( m$_{i}$φ$_{i}$ ) t$_{i}$ + α$_{i}$ − 1 20