From: Matthias Troyer (troyer_at_[hidden])
Date: 2008-01-18 05:52:27
On 16 Jan 2008, at 16:49, Milosz Marian Hulboj wrote:
> Hello,
>
> I was looking through the documentation of boost.accumulators for
> calculating the variance in one pass. It seems that for so
> called 'immediate variance' some approximation is being introduced.
> However
> I think that it is not necessary (unless there is a hidden purpose?)
> and
> incremental calculation can be done according to the substitution
> schema
> described here:
> http://planetmath.org/encyclopedia/OnePassAlgorithmToComputeSampleVariance.html
If I remember the original design discussion correctly the reason was
the following: the recurrence relation you refer to is more complex
and in addition needs a special case for he first sample. One thus
needs to test each time whether the sample count is 1 or larger, and
do more computations. Since the key requirement of the library was to
have the highest possible efficiency, the simplified approximate
equation was used that does not require an if and is faster. This is
actually okay since the error introduced is small compared to the
unavoidable sampling error.
You should have no problem, however, to implement your own variant of
the variance, e.g. variance_(accurate_immediate), using the equation
you refer to, if you should for some reason need the extra accuracy.
Matthias