small counts although the mass will be spread over thousands of categories leading to very minute differences. 5 Conclusions Sampling bias is a ubiquitous problem in studying biological problems. This work focuses on a general biasing mechanism of which data generation from in SAGE is a protype. We present three hierarchical models which provide posterior inference for the biased sampling model given in eq. (3). This work compliments earlier work by Gilchrist et al. (2007) in two notable ways. First, it provides a flexible and efficient methodology which extends the range of the prior distributions that are available. It is important to point out the effect of the typical flat prior α = 1 on inference: analogously to the binomial case (Christensen, 1997), this prior assumes that each category was seen once in previous experiments, a very strong assumption due to the small size of the tag sample compared to the number of categories. The result is that the prior overwhelms the data for many of the categories. In the context of SAGE, it may be more appealing to the scientist to choose a weaker prior such as α = 1 /k , which, as we’ve seen, gives the actual data more voice. Because the analytical approximations of Gilchrist et al. (2007) do not extend easily to this regime of priors, the simulation based results presented here are increasingly valuable. Second, the more robust methodology presented here provides a foundation for extending the analysis to include more realistic models of the tag formation process (such as the inclusion of transcription or sequencing errors) or more complex priors. Our approach may be contrasted with Morris et al. (2003), who investigated joint estima- tors of the relative proportions of different mRNA transcripts in SAGE experiments based on posterior inference from a conjugate Dirichlet-Multinomial model. They note that while the shrinkage properties of the posterior mean provide improved average inference with respect 23