[Numpy-discussion] var bias reason?

Charles R Harris charlesr.harris@gmail....
Wed Oct 15 12:09:55 CDT 2008


On Wed, Oct 15, 2008 at 9:19 AM, David Cournapeau <cournape@gmail.com>wrote:

> On Wed, Oct 15, 2008 at 11:45 PM, Travis E. Oliphant
> <oliphant@enthought.com> wrote:
> > Gabriel Gellner wrote:
> >> Some colleagues noticed that var uses biased formula's by default in
> numpy,
> >> searching for the reason only brought up:
> >>
> >>
> http://article.gmane.org/gmane.comp.python.numeric.general/12438/match=var+bias
> >>
> >> which I totally agree with, but there was no response? Any reason for
> this?
> > I will try to respond to this as it was me who made the change.  I think
> > there have been responses, but I think I've preferred to stay quiet
> > rather than feed a flame war.   Ultimately, it is a matter of preference
> > and I don't think there would be equal weights given to all the
> > arguments surrounding the decision by everybody.
> >
> > I will attempt to articulate my reasons:  dividing by n is the maximum
> > likelihood estimator of variance and I prefer that justification more
> > than the "un-biased" justification for a default (especially given that
> > bias is just one part of the "error" in an estimator).    Having every
> > package that computes the mean return the "un-biased" estimate gives it
> > more cultural weight than than the concept deserves, I think.  Any
> > surprise that is created by the different default should be mitigated by
> > the fact that it's an opportunity to learn something about what you are
> > doing.    Here is a paper I wrote on the subject that you might find
> > useful:
> >
> >
> https://contentdm.lib.byu.edu/cdm4/item_viewer.php?CISOROOT=/EER&CISOPTR=134&CISOBOX=1&REC=1
> > (Hopefully, they will resolve a link problem at the above site soon, but
> > you can read the abstract).
>
> Yes, I hope too, I would be happy to read the article.
>
> On the limit of unbiasdness, the following document mentions an
> example (in a different context than variance estimation):
>
>
> http://www.stat.columbia.edu/~gelman/research/published/badbayesresponsemain.pdf<http://www.stat.columbia.edu/%7Egelman/research/published/badbayesresponsemain.pdf>
>
> AFAIK, even statisticians who consider themselves as "mostly
> frequentist" (if that makes any sense) do not advocate unbiasdness as


Frequently frequentist?

Chuck
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