[R] gaussian error propagation

Martin Maechler maechler at stat.math.ethz.ch
Tue Oct 19 10:11:51 CEST 2004

```>>>>> "Bernhard" == Bernhard Reiter <ockham at gmx.net>
>>>>>     on Tue, 19 Oct 2004 06:54:59 +0200 writes:

Bernhard> Dear list, I'm intending to use R (1.9.0 installed
Bernhard> on my linux machine) for my applied experimental
Bernhard> physics course, requiring it to do rather basic
Bernhard> statistical things (like calculation of mean,
Bernhard> std-deviation and some linear fitting).  There is,
Bernhard> though, a task for which I haven't found a
Bernhard> solution for after some days of search: in
Bernhard> experiments involving multiple (supposedly)
Bernhard> independent measurements I am required to
Bernhard> calculate the total error according to Gaussian
Bernhard> error propagation law.  [Sqrt (Sum of (squares of
Bernhard> (partials(mean) times corresponding std-dev) ) )]
Bernhard> After failing to find an appropriate function,
Bernhard> I've started trying to build my own (something
Bernhard> that takes a (mathematical) function, does the
Bernhard> partial derivations, takes the corresponding mean
Bernhard> values and sd's (i.e. from a data frame) as
Bernhard> arguments and does the remaining necessary
Bernhard> calculations.  However, even my most basic
Bernhard> experiments with D() and derive() failed, though I
Bernhard> stuck to the derive() help page and the FAQ, but
Bernhard> (x and y unspecified,) typing
>> D(expression(x^2), "x")
Bernhard> yields 0

not for me, see below
Have you accidentally redefined D() to be something else?

> (dd <- D(expression(x^2), "x"))
2 * x
> str(dd)
language 2 * x
> x <- 1:3
> eval(dd)
[1] 2 4 6
>

Bernhard>  And so does derive (that is, for the
Bernhard> gradients; this time x and y set to integer
Bernhard> values, as R complains about failing objects
Bernhard> otherwise), when, i.e., I do
>> eval(derive(expression(x*y), c("x","y")))

Bernhard> I'd be very glad if anybody could help me with
Bernhard> this rather strange behaviour and tell me if/what
Bernhard> I'm doing wrong and if maybe there's an even
Bernhard> simpler way to perform gaussian error propagation.

Bernhard> Greetings, Ockham

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