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This is probably a basic question but I will ask it anyway b/c Im stuck. I do bird research and I have bird density estimates for thousands of sampled patches along with the associated variance. To estimate the total population size of all my sample patches I need to multiply the bird density of each patch times the area of each patch:

0.45 birds/ha*3.97ha=1.78 birds/patch.

density variance=.0064

I'm then adding all the #birds/patch up to come up with the total population size:

p1(1.78 birds/patch)+p2(6.50 birds/ha)+...=total population size

Anyway, I need to account for the sampling variance of each patch so that I can come up with a reasonable confidence interval in the end, as opposed to an artificially narrow one by just using the SE of all the birds/patch. Based on the literature, I think I need to use the formula:

c^2var(theta)

where var is the density variance and theta is the number of ha however it's unclear to me how to calculate c^2. I think it is a partial derivative of the density estimate but Im having trouble at this point...

Any help using the above numbers (not using math notation) would greatly help me!

Thank you in advance.

Im using this paper "APPROXIMATING VARIANCE OF DEMOGRAPHIC PARAMETERS USING THE DELTA METHOD: A REFERENCE FOR AVIAN BIOLOGISTS" by Larkin Powell as my primary guide.

Nahanian
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  • Provide some link or reference to give more context of what you're looking for? The delta method comes into play when you have some random variable $X$ which is asymptotically normal, some function $f$ and some $Y = f(X)$. The delta method allows you to find the asymptotic distribution of $Y$. – Matthew Gunn Apr 03 '17 at 22:14
  • Im using this paper "APPROXIMATING VARIANCE OF DEMOGRAPHIC PARAMETERS USING THE DELTA METHOD: A REFERENCE FOR AVIAN BIOLOGISTS" by Larkin Powell as my guide. – Nahanian Apr 04 '17 at 13:46
  • @Nahanian, I just read the nice paper by Larkin Powell, I understand the delta method fairly well but it is unclear to me what p1 and p2, ..., in your notations in the post represent, are these known constants? – Lucas Roberts Jul 28 '17 at 18:10

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