- #1

Hepth

Gold Member

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$$F[x,a,b]$$

I am trying to find the error correlation between the function at one point and another.

For example, if I have the function at F[0,a,b] and F[0.0001,a,b] the errors should be highly correlated (nearly 1) if treated as different functions/inputs, assuming a smooth function in "x", which it is. "a" and "b" have an error that is known, and I believe I can find the correlation between "a" and "b" using external means. (I have a LOT of functions to use for that)

So if I define two functions

$$F_1[a,b] = F[0,a,b]$$

$$F_2[a,b] = F[0.1,a,b]$$

How can I find the correlation ##\sigma_{F_1 F_2}##? Even approximately would be fine. The function isn't algebraic, but programmatic in nature, though numerical derivatives are well-behaved due to its smoothness.

In the end really the function is going to be ##F[x,a_1,a_2,...,a_{11}]## But I assume if I can do it with 2 variables I can do it with more. Again, the variables "a","b","a_n" are not independent.