Collecting statistics for time dependent data?

Collecting statistics for time dependent data?

[Raimondo Giammanco]

Hello,

 I was wondering if there is a way to compute "running" statistics with
gsl.

 Consider a time dependent simulation where at each time-step you
compute a vector/matrix of data, and you want to compute the 
sample mean, but using only one additional vector for data storage.

Is it possible to adapt the gsl code to work in this conditions to
produce a stable mean without before storing all the vectors
and after using gsl_stats_mean?

I apologize in advance if it is not an interesting question, or 
if it has already been answered elsewhere.

Best Regards

-- 
Raimondo Giammanco <rongten@member.fsf.org>

Re: Collecting statistics for time dependent data?

[John Lamb]

Raimondo Giammanco wrote:
> Hello,
> 
>  I was wondering if there is a way to compute "running" statistics with
> gsl.
> 
Yes you can do it, but there's nothing in GSL that does it and its eay 
enough that you don't need GSL. Something like (untested)

double update_mean( double* mean, int* n, double x ){
   if( *n == 1 )
     *mean = x;
   else
     *mean = (1 - (double)1 / *n ) * *mean + x / n;
}

will work and you can derive a similar method for updating the variance 
using the usual textbook formula.

var[x] = (1/n) sum x^2_i - mean(x)^2

I don't know if there is a method that avoids the rounding errors. I 
don't know why so many textbooks repeat this formula without the 
slightest warning that it can go so badly wrong.

-- 
JDL

Re: Collecting statistics for time dependent data?

[Luke Stras]

On Thu, Dec 09, 2004 at 12:53:49PM +0100, Raimondo Giammanco wrote:
> Hello,
> 
>  I was wondering if there is a way to compute "running" statistics with
> gsl.
> 
>  Consider a time dependent simulation where at each time-step you
> compute a vector/matrix of data, and you want to compute the 
> sample mean, but using only one additional vector for data storage.

To the best of my knowledge, GSL doesn't have any routines to this.
However, I would recommend:

@Article{west79,
  author =       {D.H.D. West},
  title =        {Updating Mean and Variance Estimates: An Improved 
                  Method},
  journal =      {Comm. ACM},
  year =         1979,
  volume =       22,
  number =       9,
  pages =        {532-535},
  month =        {September}
}

@Article{chan79,
  author =       {T.F. Chan and J.G. Lewis},
  title =        {Computing Standard Deviations: Accuracy},
  journal =      {Comm. ACM},
  year =         1979,
  volume =       22,
  number =       9,
  pages =        {526-531},
  month =        {September}
}

I used to have some (non-GSL) code lying around to implement West's
method, but I can't find it anywhere.  It wasn't very complex, that's
for sure.

-- 
Luke Stras <stras@utias.toronto.edu>
"The meek can have the Earth; the rest of us have other plans" 
  --Henry Spencer

Re: Collecting statistics for time dependent data?

[James Theiler]

On Thu, 9 Dec 2004, John Lamb wrote:

] Raimondo Giammanco wrote:
] > Hello,
] > 
] >  I was wondering if there is a way to compute "running" statistics with
] > gsl.
] > 
] Yes you can do it, but there's nothing in GSL that does it and its eay 
] enough that you don't need GSL. Something like (untested)
] 
] double update_mean( double* mean, int* n, double x ){
]    if( *n == 1 )
]      *mean = x;
]    else
]      *mean = (1 - (double)1 / *n ) * *mean + x / n;
] }
] 
] will work and you can derive a similar method for updating the variance 
] using the usual textbook formula.
] 
] var[x] = (1/n) sum x^2_i - mean(x)^2
] 
] I don't know if there is a method that avoids the rounding errors. I 
] don't know why so many textbooks repeat this formula without the 
] slightest warning that it can go so badly wrong.
] 
]

Stably updating mean and variance is remarkably nontrivial.  There was
a series of papers in Comm ACM that discussed the issue; the final one
(that I know of) refers back to the earlier ones, and it can be found
in D.H.D. West, Updating mean and variance estimates: an improved
method, Comm ACM 22:9, 532 (1979)  [* I see Luke Stras just sent this
reference! *].  I'll just copy out the pseudocode since the paper is
old enough that it might not be easy to find.  This, by the way, is
generalized for weighted data, so it assumes that you get a weight and
a data value (W_i and X_i) that you use to update the estimates XBAR
and S2:

    SUMW = W_1
    M = X_1
    T = 0
    For i=2,3,...,n 
    {
       Q = X_i - M
       TEMP = SUM + W_i    // typo: He meant SUMW
       R = Q*W_i/TEMP
       M = M + R
       T = T + R*SUMW*Q
       SUMW = TEMP
    }
    XBAR = M
    S2 = T*n/((n-1)*SUMW)



jt 

-- 
James Theiler            Space and Remote Sensing Sciences
MS-B244, ISR-2, LANL     Los Alamos National Laboratory
Los Alamos, NM 87545     http://nis-www.lanl.gov/~jt