Re: [boost] [rfc] Inexact quantities arithmetics

From: Lewis Hyatt (lhyatt_at_[hidden])
Date: 2007-07-10 00:10:09

> 6. Correlations are not considered; instead, worst case is always assumed.
> For example:
>      (mx +- dx) + (my +- dy) gives ((mx + my) +- (dx + dy), not ((mx +
> my) +- sqrt(dx*dx + dy*dy);

If x and y are uncorrelated normally distributed variables, then the variance of
x+y is the sum of the variances of x and y. This implies the latter error law,
which you say you don't implement. So setting the error to (dx+dy) has nothing
to do with ignoring correlations. It is hard for me to imagine a case when
simply adding the errors like this is in any way meaningful. Note, in
particular, that this error law would imply no benefit whatsoever to averaging
the results from many observations together... you would get the same error as
you would from any one trial. This is the same as assuming the quantities mx and
my are Cauchy-distributed, which is a very odd assumption for the general case.

-Lewis