was viewed as an unbiased sample of the mRNA population. As pointed out by Gilchrist et al. (2007), this equivalence only holds when all genes have the same tag formation probability. Given the variation between genes, this condition will never be met. Consequently, genes with greater than average tag formation probabilities will be over-represented in the tag pool. Conversely, tags with a lower than average tag formation probability will be under- represented. This sampling bias in the formation of the tag pool, however, can be estimated and used to correct the inferences made from the SAGE data. The first step in adjusting for this bias is the calculation of the tag formation probabilities for every gene in the genome. 

## 3.1 Biased Sampling and Tag Formation Probabilities 

As pointed out in Section 2, only cDNA that is attached to a streptavidin bead is retained during the experimental process. As a result, tags are created from the 3’ most AE site that is actually cleaved (Figure 1). Let k$_{i}$ be the number of restriction enzyme sites which may be cleaved by the AE on mRNA generated from gene i , let p be the probability the AE will cleave a site, and assume that cleavage probability is independent between sites and does not vary between genes. If we label sites 1 through k$_{i}$ starting at the 3’ most site (i.e. the site closest to the bead; see Figure 1). It follows that the probability of generating a tag through AE cleavage at site j ∈ { 1 , . . . , k$_{i}$ } is (1 − p$_{i}$ ) j − $^{1}$p$_{i}$ . This corresponds to the probability of no cleaving in sites 1 to j − 1, and a cleaving at site j . Note that this probability is independent of what happens at the AE sites 5’ from the j th site. Thus, the probability of creating a tag at site j on an mRNA generated from gene i follows a geometric distribution. The fact that the expected distribution of tags varies with AE cleavage probability p can be used to estimate p from the set of intra-genic tag distributions (Gilchrist et al., 2007). 

If the set of tags which can be created from the AE sites within a gene’s mRNA trascript are all informative (i.e. can be uniquely assigned to a single gene), the probability of gener- 

