[SciPy-User] kriging module

Robert Kern robert.kern@gmail....
Sat Nov 20 17:35:53 CST 2010


On Sat, Nov 20, 2010 at 17:08, Gael Varoquaux
<gael.varoquaux@normalesup.org> wrote:
> On Sat, Nov 20, 2010 at 04:59:41PM -0600, Robert Kern wrote:
>> > Sorry, I should have said 'Gaussian process regression', which is the
>> > full name, and is an equivalent to Kriging. Gaussian processes in
>> > themself are a very large class of probabilistic models.
>> > AFAICT, PyMC does not have any Gaussian process regression, and it does
>> > seem a bit outside its scope.
>
>> I'm pretty sure it does. See section 1.4 "Nonparametric regression"
>> and 2.4 "Geostatistical example" in the GP User's Guide:
>
>>   http://pymc.googlecode.com/files/GPUserGuide.pdf
>
> Yes, you are right. My bad. The good news is that it means that the name
> is not too badly overloaded.
>
> I see that they do the estimation by sampling the posterior, whereas the
> proposed contribution in the scikit simply does a point estimate using
> the scipy's optimizers. I guess that PyMC's approach gives a full
> posterior estimate, and is thus richer than the point estimate, but I
> would except it to be slower. I wonder if they are any other fundemental
> differences (I don't know Gaussian processes terribly well).

Well, the posterior is always Gaussian, so point estimates with 1-SD
error bands characterize the posterior perfectly well! pymc.gp does
point estimates, too. See the Mean.observe() method. It used to live
as a separate package by another author before they decided to merge
it into PyMC.

But yes, kriging is a specialization of GP regression by another name.
The main distint features of kriging are that the covariance functions
usually take a particular form (a nonzero variance called the "nugget"
infinitesimally off of 0 and increasing smoothly to a limiting value
called the "sill" far from 0), and the covariance function is often
estimated from the data. Oh, and no one outside of geostatistics uses
the word "kriging". ;-)

-- 
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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