where θ$_{i}$ are the frequencies of tags in the tag pool. Section 3.1 indicates that frequency of SAGE tags generated from gene i is, where, we remind the reader, that φ$_{i}$ is known and represents the probability that a mRNA strand from gene i in the group of cells will be converted into a tag and where m$_{i}$ , the quantity of interest, is the relative proportion of mRNA from gene i in those cells. Hence, the bias corrected likelihood model is, Because the vector m = { m$_{1}$, m$_{2}$, . . . m$_{k}$ } is a vector representing relative proportions, or equivalently the probability that an individual mRNA strand represents gene i , the compo- nents of m must satisfy the conditions: m$_{i}$ ≥ 0 and ∑ k i $_{=1}$m$_{i}$ = 1. Direct maximization of the likelihood with respect to the parameters m$_{i}$ is straightforward via the invariance property of the MLE. Consider the observed sample proportion ˆ θ$_{i}$ = t$_{i}$/T$_{tot}$ . Given constraints on the possible values of m$_{i}$ and equation (2), the MLE estimates of ˆ m = { ˆ m$_{1}$, ˆ m$_{2}$, . . . , ˆ m$_{k}$ } must satisfy the following equality, While estimation of the MLE is relatively straightforward, estimating confidence intervals for m is difficult. The existence of the normalization term ∑ j m$_{j}$φ$_{j}$ in the denominator of the l.h.s. of eq. (4) makes computation of the information matrix taxing, particularly for the large dimensional vectors encountered when working with SAGE data (i.e. k is of the order 10 3 to 10 $^{4}$). In addition, because the number of categories is generally within an order 11 k ∑ i ˆ θ$_{i}$ φ$_{i}$ = 1 ∑ k i ˆ m$_{i}$φ$_{i}$ . (4) P ( T | m ) = ( T$_{tot}$ t$_{1}$, t$_{2}$, . . . , t$_{k}$$^{)}$$^{∏}$ i ( m$_{i}$φ$_{i}$ ∑ j m$_{j}$φ$_{j}$$^{)}$$^{t$_{j}$}$ (3) θ$_{i}$ = m$_{i}$φ$_{i}$ ∑ j m$_{j}$φ$_{j}$ (2)