[SciPy-user] Iterative proportional fitting
James Coughlan
coughlan@ski....
Thu Jan 8 18:14:05 CST 2009
You can use the maximum entropy to estimate a joint distribution given
marginals (or arbitrary functions of marginals), e.g. see pdf tutorial
on "Maximum Entropy Distributions and Their Relationship to Maximum
Likelihood
<http://www.ski.org/Rehab/Coughlan_lab/General/Tutorials/MaxEnt.pdf> "at:
http://www.ski.org/Rehab/Coughlan_lab/General/Tutorials.html
Assuming your marginals are defined numerically (e.g. histograms or
means/variances/moments) this should work. Once you've set up the
problem this way, you can solve it numerically using gradient descent.
Best,
James
Dorian wrote:
> Thanks for your quick response. You are right , I've tried that, but
> copula are limited only
> to the case that the marginal distributions are uniform over the
> interval zero to one.
>
> As I read from literature IPF method is more general and can be
> applied also with marginal
> distributions, not limited to the interval zero to one .
>
> Thanks again,
>
> Dorian
>
>
>
>
>
>
>
> 2009/1/9 Robert Kern <robert.kern@gmail.com
> <mailto:robert.kern@gmail.com>>
>
> On Thu, Jan 8, 2009 at 17:06, Dorian <wizzard028wise@gmail.com
> <mailto:wizzard028wise@gmail.com>> wrote:
> > Hi all,
> > I have some marginal functions densities and I'm looking to the
> good way to
> > find their join density function.
>
> There are potentially an infinite number of such joint density
> functions that have the same marginal densities. Adding some
> constraints, like a correlation between two variables, helps, but it's
> still an ill-defined problem.
>
> > I would want to know if there is any package or script in Scipy
> for
> > iterative proportional fitting (IPF) .
> > Or any web link to help me start.
>
> No, there is nothing in scipy for this. I think IPF applies more to
> data than to distributions, per se. Estimating a joint distribution
> from marginal distribution is usually called a copula, in my
> experience.
>
> http://en.wikipedia.org/wiki/Copula_(statistics)
> <http://en.wikipedia.org/wiki/Copula_%28statistics%29>
>
> --
> Robert Kern
>
> "I have come to believe that the whole world is an enigma, a harmless
> enigma that is made terrible by our own mad attempt to interpret it as
> though it had an underlying truth."
> -- Umberto Eco
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--
-------------------------------------------------------
James Coughlan, Ph.D., Scientist
The Smith-Kettlewell Eye Research Institute
Email: coughlan@ski.org
URL: http://www.ski.org/Rehab/Coughlan_lab/
Phone: 415-345-2146
Fax: 415-345-8455
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