In archaeology, artefacts are commonly classified in categories according to certain criteria (those may include manufacturing technique, decoration, function, chronology, etc).
I am trying to estimate the probability that objects of a certain category $C$ are absent from the site, even after group $G$ has been collected and no category $C$ objects were found. Group $G$ is a “sample” from the group of all objects that were used at the site in a certain moment (actual examples are a waste dump from a house, and domestic tools "frozen" under a collapsed building). Archaeologists will recover all artefacts from the soil but it is an established fact that not all objects will survive, and that we will never recover all of them.
The data I have include some prior knowledge about the (relative and absolute) abundance of $C$: the amount and proportion of $C$ in all groups where it is present, and the total amount of artefacts in all groups, including ones where $C$ is not found (I have other related data but these variables seem the relevant ones). Groups aren't generally very large, around 300-500. Objects of category $C$ account for 1-3% of artefacts when they are found. I expect that the larger the “sample” the higher the probability of absence will be.
A professor of statistics suggested me that methods used by ecologists might be appropriate, e.g. the work of McBride & Johnstone found here: http://www.nzes.org.nz/nzje/contents.php?volume_issue=j35_2 (Credible Interval Value). Is is feasible to apply these methods to the above problem using R, and how? If not, what other methods are appropriate?
