ating any of the possible tags from the i th category of mRNA is When ambiguous tagging sites occur within a gene’s mRNA transcript, say sites l and m , these sites are simply excluded from the summation over j in eq. (1). The reduction in φ$_{i}$ due to tag ambiguity is greatest when an ambiguous tag is formed at the 3’ most AE site (site 1 in Figure 1) and is least when such a tag occurs in the 5’ most AE site (site k$_{i}$ ). But note that it is possible for transcripts to have multiple ambiguous AE tag formation sites. For purposes of our analysis, we will assume that the value of φ$_{i}$ has been estimated for all genes and treat these as known constants (see Gilchrist et al. (2007) for a more details on these calculations). The variation in the tag formation probability between genes stems from the two basic facts. First, genes vary in the number of AE sites they contain. Second, genes also vary in the number and location of AE sites which are ambiguous. As a result the tag pool represents a biased sample of the mRNA population of interest. The degree of bias exhibited is a function of both the distribution of tag formation probabilities across the genome, and the distribution of these genes within the mRNA population itself, as we will now demonstrate. As discussed earlier, an obvious model for the observed tag data is the multinomial distri- bution. Let T$_{tot}$ = ∑ k i =1 t$_{i}$ be the total count of all observed tags. Then 3.2 Maximum Likelihood and the Joint Posterior Distribution P ( T | θ ) = ( T$_{tot}$ t$_{1}$, t$_{2}$, . . . , t$_{k}$$^{)}$$^{∏}$ i θ t$_{i}$ i 10 φ$_{i}$ = k$_{i}$ ∑ j =1 (1 − p ) j − $^{1}$p = 1 − (1 − p ) $^{k$_{i}$}$. (1)