[SciPy-User] max likelihood

David Goldsmith d.l.goldsmith@gmail....
Mon Jun 21 19:03:51 CDT 2010


On Mon, Jun 21, 2010 at 4:10 PM, <josef.pktd@gmail.com> wrote:

> On Mon, Jun 21, 2010 at 7:03 PM, David Goldsmith
> <d.l.goldsmith@gmail.com> wrote:
> > On Mon, Jun 21, 2010 at 3:17 PM, Skipper Seabold <jsseabold@gmail.com>
> > wrote:
> >>
> >> On Mon, Jun 21, 2010 at 5:55 PM, David Goldsmith
> >> <d.l.goldsmith@gmail.com> wrote:
> >> > On Mon, Jun 21, 2010 at 2:43 PM, Skipper Seabold <jsseabold@gmail.com
> >
> >> > wrote:
> >> >>
> >> >> On Mon, Jun 21, 2010 at 5:34 PM, David Goldsmith
> >> >> <d.l.goldsmith@gmail.com> wrote:
> >> >> > On Mon, Jun 21, 2010 at 2:17 PM, eneide.odissea
> >> >> > <eneide.odissea@gmail.com>
> >> >> > wrote:
> >> >> >>
> >> >> >> Hi All
> >> >> >> I had a look at the scipy.stats documentation and I was not able
> to
> >> >> >> find a
> >> >> >> function for
> >> >> >> maximum likelihood parameter estimation.
> >> >> >> Do you know whether is available in some other namespace/library
> of
> >> >> >> scipy?
> >> >> >> I found on the web few libraries ( this one is an
> >> >> >> example http://bmnh.org/~pf/p4.html<http://bmnh.org/%7Epf/p4.html> )
> having it,
> >> >> >> but I would prefer to start playing with what scipy already offers
> >> >> >> by
> >> >> >> default ( if any ).
> >> >> >> Kind Regards
> >> >> >> eo
> >> >> >
> >> >> > scipy.stats.distributions.rv_continuous.fit (I was just working on
> >> >> > the
> >> >> > docstring for that; I don't believe my changes have been merged; I
> >> >> > believe
> >> >> > Travis recently updated its code...)
> >> >> >
> >> >>
> >> >> This is for fitting the parameters of a distribution via maximum
> >> >> likelihood given that the DGP is the underlying distribution.  I
> don't
> >> >> think it is intended for more complicated likelihood functions (where
> >> >> Nelder-Mead might fail).  And in any event it will only find the
> >> >> parameters of the distribution rather than the parameters of some
> >> >> underlying model, if this is what you're after.
> >> >>
> >> >> Skipper
> >> >
> >> > OK, but just for clarity in my own mind: are you saying that
> >> > rv_continuous.fit is _definitely_ inappropriate/inadequate for OP's
> >> > needs
> >> > (i.e., am I _completely_ misunderstanding the relationship between the
> >> > function and OP's stated needs), or are you saying that the function
> >> > _may_
> >> > not be general/robust enough for OP's stated needs?
> >>
> >> Well, I guess it depends on exactly what kind of likelihood function
> >> is being optimized.  That's why I asked.
> >>
> >> My experience with stats.distributions is all of about a week, so I
> >> could be wrong. But here it goes... rv_continuous is not intended to
> >> be used on its own but rather as the base class for any distribution.
> >> So if you believe that your data came from say an Gaussian
> >> distribution, then you could use norm.fit(data) (with other options as
> >> needed) to get back estimates of scale and location.  So
> >>
> >> In [31]: from scipy.stats import norm
> >>
> >> In [32]: import numpy as np
> >>
> >> In [33]: x = np.random.normal(loc=0,scale=1,size=1000)
> >>
> >> In [34]: norm.fit(x)
> >> Out[34]: (-0.043364692830314848, 1.0205901804210851)
> >>
> >> Which is close to our given location and scale.
> >>
> >> But if you had in mind some kind of data generating process for your
> >> model based on some other observed data and you were interested in the
> >> marginal effects of changes in the observed data on the outcome, then
> >> it would be cumbersome I think to use the fit in distributions. It may
> >> not be possible.   Also, as mentioned, fit only uses Nelder-Mead
> >> (optimize.fmin with the default parameters, which I've found to be
> >> inadequate for even fairly basic likelihood based models), so it may
> >> not be robust enough.  At the moment, I can't think of a way to fit a
> >> parameterized model as fit is written now.  Come to think of it though
> >> I don't think it would be much work to extend the fit method to work
> >> for something like a linear regression model.
> >>
> >> Skipper
> >
> >
> > OK, this is all as I thought (e.g., fit only "works" to get the MLE's
> from
> > data for a *presumed* distribution, but it is all-but-useless if the
> > distribution isn't (believed to be) "known" a priori); just wanted to be
> > sure I was reading you correctly. :-)  Thanks!
>
> MLE always assumes that the distribution is known, since you need the
> likelihood function.
>

I'm not sure what I'm missing here (is it the definition of DGP? the meaning
of Nelder-Mead? I want to learn, off-list if this is considered "noise"):
according to my reference - Bain & Englehardt, Intro. to Prob. and Math.
Stat., 2nd Ed., Duxbury, 1992 - if the underlying population distribution is
known, then the likelihood function is well-determined (although the
likelihood equation(s) it gives rise to may not be soluble analytically, of
course).  So why doesn't the OP knowing the underlying distribution (as your
comment above implies they should if they seek MLEs) imply that s/he would
also "know" what the likelihood function "looks like," (and thus the
question isn't so much what the likelihood function "looks like," but what
the underlying distribution is, and thence, do we have that distribution
implemented yet in scipy.stats)?

DG


> It's not non- or semi-parametric.
>
> Josef
>
> >
> > DG
> >
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-- 
Mathematician: noun, someone who disavows certainty when their uncertainty
set is non-empty, even if that set has measure zero.

Hope: noun, that delusive spirit which escaped Pandora's jar and, with her
lies, prevents mankind from committing a general suicide.  (As interpreted
by Robert Graves)
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