Estimating the number of sources of population using sampling techniques

Question

Background of the problem:

There are about 500,000 uncatalogued specimen in a laboratory. These specimens are gathered from across the world. We want to answer two questions:

1. How many different countries these 500,000 specimen come from?
2. How many specimen come from each of the countries.

The specimen are not stored in any specific order currently. There are qualified personnel who can determine the origin of the specimen but their time is limited. We are constrained by budget and in the process of working out how much time can spend sampling but I don't think we can collect information on more than 1000-2000 specimen.

I need to come up with a sampling strategy answer the above questions with a reasonable level of accuracy.

Any materials/guidance on the strategies and sampling estimators I can leverage would be quite helpful.

Answer 1

If you have zero information (this is not usually the case in real-life) about the specimens before its inspection there is no better sampling strategy. The best thing you can do is analyse the most specimens you can.

For question 1 and 2, the a priori knowledge you could have about how and where the set of specimens came into the lab can change the way you model the problem. In real-life it is highly unlikely not having any context (probably there have been recorded projects to obtain the specimens).

If you really have no information, there are some biology articles on the estimation of discovering new species that draw a similar framework such as https://projecteuclid.org/euclid.aos/1176345651 or https://academic.oup.com/biomet/article-abstract/94/4/769/246082.

You have the advantage of knowing the upper bound for your countries (there are around 200 if we don't consider historic changes).

I want to underline the importance of context because a sample of 1000-2000 out of 500000 can lead you to really inaccurate results without it. The context also will narrow down the problem and help you get better advise in this site.