From help-octave-request at bevo dot che dot wisc dot edu Sun Mar  2 13:50:37 2003
Subject: Re: Covariance Question
From: Mike Miller <mbmiller at taxa dot epi dot umn dot edu>
To: Dirk Eddelbuettel <edd at debian dot org>
cc: "Al Piszcz 'peesh'" <apiszcz at solarrain dot com>, help-octave@bevo.che.wisc.edu
Date: Sun, 2 Mar 2003 13:49:32 -0600 (CST)

On Sun, 2 Mar 2003, Dirk Eddelbuettel wrote:

> edd at chibud:~> octave2.1 -q
> octave2.1:1> x=[3;1;3;9];
> octave2.1:2> y=[4;4;8;8];
> octave2.1:3> cov(x,y)*(length(x)-1)/length(x)
> ans = 4
>
> The difference depends on whether you "know" that your data comes from
> a sample versus a population. See e.g.
>
> http://newton.dep.anl.gov/newton/askasci/1993/math/MATH014.HTM


Right.  It's the N v. N-1 effect.  Use of N produces the maximum
likelihood estimator for multivariate normal data.  It has good properties
and is, in some ways, superior to use of N-1.  That's another reason to
use N sometimes, not just because the entire population is known.  Still,
N-1 is used much more often, and Octave uses N-1.  I think it's the right
choice for the default behavior of the cov function.  It's also what
MATLAB does.

Mike



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