on both its tag formation probability and the distribution of these probabilities across all other genes weighted by their mRNA frequency. Gilchrist et al. (2007) derive an implicit solution for the maximum likelihood and joint posterior mode estimators of the composition of the mRNA population. However, there are a number of numerical stability issues that severely limit the range of prior parameters that can be used, i.e. those priors with appre- ciable weight relative to the observed sample sizes. There is also the restrictive assumption that the contribution of an individual gene to the weighted average is small in order to derive approximations for the marginal credible sets for a given gene. We introduce several new hierarchical models for the posterior distribution of the mRNA proportions given the bias in the observed data. These methods are more robust, flexible, and require fewer assumptions than the analytic approach outlined in Gilchrist et al. (2007). In addition to the bias introduced through the tag formation process itself, other steps in the experimental process can introduce errors which will affect the ability to interpret SAGE data. These include sampling error, sequencing error, non-uniqueness and non-randomness of tag sequences (Stollberg et al., 2000). For example, the use of PCR to amplify mRNA samples can introduce copying errors into tag sequences. Tags are identified via DNA sequencing, which is an imperfect processes and errors occur on a per nucleotide basis. As a result the error rate depends on the length of the tag’s generated. A number of sophisticated techniques have been developed to correct for such errors (Colinge & Feger, 2001; Akmaev & Wang, 2004; Beissbarth et al., 2004). In this study we ignore such complications but believe that it is also possible to address these sources of error by incorporating them into a more complicated model of the experimental process. Because we are using SAGE data as an illustration, Section 2 describes the experimental process used to generate a SAGE data set as well as the sources of biases that can result and additional sources of errors. Section 3 discusses the basic sampling and inference. Section 3.1 introduces a model for tag formation, and discusses the variation in tag formation. It 5