[SciPy-User] max likelihood

Skipper Seabold jsseabold@gmail....
Mon Jun 21 17:17:40 CDT 2010

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 ) 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.


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