Re: [boost] [rfc] Inexact quantities arithmetics

From: Jeremy Maitin-Shepard (jbms_at_[hidden])
Date: 2007-07-10 01:03:43

Lewis Hyatt <lhyatt_at_[hidden]> writes:

>> 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.

It seems that the error term may be intended to mean an exact
upper/lower bound, not a variance.

-- 
Jeremy Maitin-Shepard