What do NaN uncertainties mean?

[Melissa-Iacovidou]

I'm using the Measurements.jl package to error propagate through multiple calculations including integrations (quadgk, cuba). It works well but there is an instance where I get results with ± NaN as uncertainties. Why is this happening?

[giordano]

Probably you get a NaN somewhere in your calculations (0/0 or Inf - Inf) which poisons the uncertainty. What's the physical meaning of a NaN uncertainty? Probably not much.

Would you be able to share your code?

[giordano]

The error of exp(x_0) is given by the product of the derivative of exp(x), evaluated at x = x_0, times the error of x_0: exp(-Inf) = 0 and the error is Inf: 0 * Inf = NaN

[Melissa-Iacovidou]

You are right, thanks for all the help!

[giordano]

I'm sorry for not having being able to solve your issue, but unfortunately things get numerically tricky at pathological values 😞 even though in some cases limits may be well defined, mathematically, computers are dumb and 0 * Inf always results in NaN (unless one adds a more complex algebra to the system...)

[Melissa-Iacovidou]

No worries, it seems like if I numerically integrate until say 10^3 instead of Inf, the results are essentially the same, and I get an actual error. I checked the value of my integral from 10^3 to Inf and it gives me zero, so the contribution seems to be negligible. I think this could be a temporary fix at the moment. Might consider doing a log transformation or something.

[giordano]

Yeah, if the integral between your threshold and Inf is less than the uncertainty you'd get, it does make sense to stop earlier!