another type of restriction enzyme), but is invariant within an experiment. Initially SAGE tags were 14 bp long. However, four of these bp reflect the cutting motif of the AE and, as a result, were shared by all tags. Experimental advances have been able to extend the tag length to over 20 bp. For example, ‘SuperSAGE’ techniques can lead to tags up to 26 bp long (Matsumura et al., 2003, 2006). Unfortunately, extending the length of a tag comes at a cost (Stollberg et al., 2000). This is because neither the reverse transcription, the PCR amplification, or sequencing process is error free. For example, Velculescu et al. (1997) esti- mate that the sequencing error rate of a tag is 0 . 007 / bp, thus the probability of obtaining an error free tag decreases geometrically with sequence length, ranging from approximately 10% to 15% in 14 and 22 bp tags, respectively. Transcription errors, either by the cell or during the conversion to cDNA or amplification by the experimentalist, can create either novel ‘orphan’ tags which cannot be mapped to a particular gene or misleading tags which are attributed to the wrong gene. 

## 3 Basic Statistical Inference 

Before the SAGE tag counts are considered, we assume that the data is processed to retain only informative tags, i.e. all ambiguous or orphan tags are removed, as is standard practice. The result can be viewed as a vector of observed tag counts for individual genes, i.e. T = ( t$_{1}$, . . . t$_{k}$ ) where k is the number of genes that contain at least one unambiguous AE site and t$_{i}$ is the sum of all counts which can be uniquely attributed to gene i . It is natural here to view this vector as a sample from a multinomial distribution with k categories. Thus T ∼ Multi ( T$_{tot}$, θ ) where θ$_{i}$ represents the frequency of gene i tags in the tag pool and T$_{tot}$ represents the total number of informative tags sequenced, i.e. T$_{tot}$ = ∑ j t$_{j}$ . Until recently, inferences about a gene’s frequency in the mRNA population, the population of interest, were assumed to be equivalent to any inferences made about its tag frequency, i.e. the tag pool 

