Re: [Boost-users] [Boost.accumulators] Immediate variance

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