# Estimating a Population from Sampling with Imperfect Detection

#### MindsEyeSifter

##### New member
Hello All, thanks for looking at my post and question. I have jumped into deep statistical and probability waters which have outstripped my current state of knowledge so any help you can render would be greatly appreciated. Here is my question:

I am trying to get an estimate of the original population in this case of archaeological sites. To do so I have two methods by which I can sample an area. Using a mathematical model I built and based on known archaeological sites in a particular region I can characterize the sites based on two parameters which affect detection: site size and artifact density. From this I can derive a mean probability of detection as well as the standard deviation and the variance. The two methods have different detection probabilities and will strongly affect the interpretation if taken into account.

In order to estimate the population (true number of archaeological sites in a region) I could simply take the mean detection probability and proportionally adjust for it, but this would not produce very robust results. I have attempted to find other equations which would allow me to more accurately estimate the original population. However I do not understand the formulas enough to be able to determine if they would apply to my data and answer the questions I am asking.

The most promising comes from Thompson and Seber's book Adaptive Sampling (1996:223-226). In example 9.3 they present a modified version of the Horvitz-Thompson estimator. Thompson and Seber modified the original to take into account imperfect detectability of the sampling methods. Attached are the pertinent pages from their book. I am not proficient at typing out the formulas so I apologize for the low rez pdf.
Basically I am having a hard time understanding what all of the variables are and what I should do with them in order to evaluate the appropriateness of this formula for my work.
I am sure I am leaving out gobs of information so if you need any clarification please ask and thanks again for all the help!

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