Robert Dodier <robert.dodier at gmail.com> writes:
> The simplest thing to do is linearize it (via derivatives) but if the
> function (sine / cosine / whatever) is noticeably nonlinear over the
> range of the uncertain variable (say more or less the middle 95% of
> mass) then linearization will be a poor approximation. This is going
> to be especially noticeable since sine / cosine have bounded ranges --
> anything near the edges of the range will be "interesting" (i.e. not
> anywhere near linear).
I'm a bit confused about this bit. This is sine/cosine rather than their
inverses. So at the edge of their output ranges, they have zero
derivative. Since the trig functions are analytic with well behaved
coefficients, I'm interested to know what can go weird?
> Just glancing at the equation, my guess is that an exact solution, if
> possible, is probably enormous and clumsy. As to approximations, the
> easiest thing is a Monte Carlo method. If you just need to get a
> result in the ballpark, that's my recommendation. Semi-numerical,
> probably more nearly exact approaches are also possible -- I can give
> you some ideas if you're interested.
I agree with this and I'd be interested to read what people have done on
the subject. Presumably cleverer than "Input noise with some
distribution. Record output distribution" ! Where should I be looking
for more information?
Rupert
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