In the lecture today in Environmental Monitoring and Audit, I mentioned the model examining how much search effort is required to be sufficiently sure of the absence of a species at a site. This was based on a paper by Brendan Wintle et al. (2012).
You can read more about this topic here, with an attempt at an intuitive interpretation of the model, and some links to other examples where the prior probability (base rate) matters.
If you are particularly keen, you can read a copy of the manuscript here.
Wintle, B.A. Walshe, T.V., Parris, K.M., and McCarthy, M.A. (2012). Designing occupancy surveys and interpreting non-detection when observations are imperfect. Diversity and Distributions 18: 417-424.