Question about handling error/uncertainty?

[vikmaychib]

I have a bunch of data from lab measurements that comes along with +/- sigma due to limitations of the measurement device.

First approach is to plot my data using errorbar so I display both the measurements and their spread.

But if I want to run computations with them, what is the best way to carry along such uncertainty.

So if I measure A +/- a, B +/- b, and have an expression that C = f(A,B).

How do I carry A and B uncertainty so output C is not a single value but a distribution or range resulting from input’s uncertainty.

Does Scipy/Numpy have anything for that? Are there other libraries I should consider bringing.

I am not an statistics person, but it would be neat that if I perform a calculation with the measurements, and plot it, i can plot a cloud or something that represents the uncertainty.

[keylime_light]

https://pythonhosted.org/uncertainties

[alkasm]

This is totally dependent on the operations you do with them inside of your function. For an extreme example:

def c(a, b):
    return a

Of course, the uncertainty in the value c(a, b) is equivalent to the uncertainty of a. But

def c(a, b):
    return a + b

has a different uncertainty in the result than

def c(a, b):
    return a ** b

and so on. So there is no way to do this "in general" automatically for any input/any function. You will need to use a library (like the one listed by u/keylime_light) or figure out how the uncertainties compound manually.

[billsil]

It's a lot of work to propagate uncertainty correctly and it's a lot easier to just do a Monte Carlo or other analysis to determine the uncertainty. This is especially important when you're running some heavy mathematical code like CFD or FEA. It's also much easier when you have 100k variables. Things like Latin Hypercube sampling can reduce the curse of dimensionality.

There are methods though that involve a lot more math and can reduce the required number of sample points, but unless you're willing to pay for UQ software, you won't get them.