[SciPy-user] Iterative proportional fitting

[James Coughlan]

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 at gmail.com 
> <mailto:robert.kern at gmail.com>>
>
>     On Thu, Jan 8, 2009 at 17:06, Dorian <wizzard028wise at gmail.com
>     <mailto:wizzard028wise at 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 at ski.org
URL: http://www.ski.org/Rehab/Coughlan_lab/
Phone: 415-345-2146 
Fax: 415-345-8455
-------------------------------------------------------