Modeling Sage data with a truncated gamma-Poisson model

We present a hierarchical Poisson model with a gamma prior and three different algorithms for estimating the parameters in the model. It turns out that the rate parameter in the gamma distribution can be estimated on the basis of a single SAGE library, whereas the estimate of the shape parameter becomes unstable. This means that the number of zero counts cannot be estimated reliably. When a bivariate model is applied to two SAGE libraries, however, the number of predicted zero counts becomes more stable and in approximate agreement with the number of transcripts observed across a large number of experiments. In all the libraries we analyzed there was a small population of very highly expressed tags, typically 1% of the tags, that could not be accounted for by the model. To handle those tags we chose to augment our model with a non-parametric component. We also show some results based on a log-normal distribution instead of the gamma distribution.By modeling SAGE data with a hierarchical Poisson model it is possible to separate the sampling variance from the variance in gene expression. If expression levels are reported at the gene level rather than at the tag level, genes mapped to multiple tags must be kept separate, since their expression levels show a different statistical behavior. A log-normal prior provided a better fit to our data than the gamma prior, but except for a small subpopulation of tags with very high counts, the two priors are similar.In Serial Analysis of Gene Expression (SAGE), mRNA is extracted from a tissue sample and converted to cDNA, from which oligonucleotides (so-called SAGE tags) at specific locations in the cDNA fragments are extracted and amplified using PCR. Those tags are either ten or seventeen bases long, depending on the experimental protocol. Sequencing the PCR product, it is possible to establish the number of copies of each tag extracted. (For an elaborate description of the technology, see Velculescu [1]). Ideally, there would