Re: propagating errors

[CdeMills]

Isak Delberth Davids wrote:
> 
> Dear all,
> 
> Do we have a tool that computes error propagation (given "initial" errors)
> as variables get computed. I read about a class @meas in Matlab, but since
> I
> do not have Matlab I cannot even teach myself its use. I am trying to
> avoid
> first writing down some tedious error propagation formulae and then coding
> them --- or is that my ultimate choice?
> 
> 

Hello Isak,
be VERY carefull about computing error propagations. You have two schools of
though:
- engineers mostly consider the error as having a continuous pdf, the errors
lies inside an interval. The difficulty of this approach is that it doesn't
scale. If you add an infinite number of variables with the same error
interval, the global error interval becomes infinite: there is a confusion
between INTERVAL and DOMAIN
- statisticians don't have a problem with a infinite domain, and associate
ranges and probability. For a gaussian pdf, which is the limiting case of
the previous example, you have 95% that the error lies between +/- 2 sigmas,
99 between +/- 3 sigmas, and so on.

So before going further, I suggest you to have a look at 
http://www.itl.nist.gov/div898/handbook/mpc/section5/mpc55.htm for
theoretical aspects, and 
http://mathworld.wolfram.com/ErrorPropagation.html
for the computational aspects. In summary:
- you should perform computations in terms of variance, which does scale
- to characterise a propagation chain, you'll have to compute the matrix of
partial derivatives around the operational point.
There is thus no such package in Octave, but contribution would be welcome
:-)

Pascal
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