Re: Kolmogorov-Smirnov test... a good overview

In article <b6ca7154-b66f-48fc-81ff-ca7dd1cd6fb6@xxxxxxxxxxxxxxxxxxxxxxxxxx>,
<lunogled@xxxxxxxxx> wrote:
On Mar 11, 5:34 pm, hru...@xxxxxxxxxxxxxxxxxxxx (Herman Rubin) wrote:
In article <7f85a8ce-1731-4d55-9aff-995df02e9...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,

<lunog...@xxxxxxxxx> wrote:
On Mar 10, 2:00 am, David Winsemius <doe_s...@xxxxxxxxxxx> wrote:
lunog...@xxxxxxxxx wrote innews:7ebb138e-8487-4fe5-ae1d-ad7b103237ad@xxxxxxxxxxxxxxxxxxxxxxxxxxxx:

................

a) At what negative power of n (the geometric mean of the size of the
two samples) do corrections to the KS distribution typically appear?
b) What are the situations where the test is likely to fail, and why?

If parameters are estimated, the distribution of the KS
statistic is greatly modified.

Could you please specify what you mean by "If parameters are
estimated"? I do not plan to use the KS test as a fit (rather as a
"check" of a fit), so my distribution will not have any fit parameters
(see further in the post).

It seems that you do fit parameters.

Also, the KS test is for one dimension. In your model
later, you have more.


So far, even the limiting
asymptotics have only been calculated by simulation, which
is harder than one might think.

Fair enough. Could you point me to a publication where this was
done?

I do not recall all of them; I think Stevens was involved,
but I do not think he was the main one.

One problem with simulation here is that the tail points
are being estimated, and it is difficult to put more
emphasis on the tails in simulation.


The level: I am a theoretical physicist (postdoc), but my knowledge
of statistics is "self-thought" with applications in mind.

Alas, this makes it much harder to understand. Statistics
is not a collection of procedures.

I have not quite figured out what your goal is.
I am trying to see to what extent the Kolmogorov-Smirnov test can be
used as a tool in the study of very high multiplicity hadronic events
(such as heavy ion collisions). Both in studying event-by-event
fluctuations and in comparing data to Montecarlo-generated events.

I understand the description given, but I still have
no idea of what data you are investigating.

Basically, momentum of particles in collisions.

Each event has anything from 80 to 600 particles (one could make bins
where the uncertainity in multiplicity is much lower), one can measure
the distribution in all three components of momentum (equivalently the
rapidity, transverse momentum, and azimuthal angle, the preferred
observables in particle physics)

I am looking for two things:

a) Are there as yet unknown correlations specific to the event
(For example clusters emitting particles), which would lead to
variations in each event's probability distribution function of
momenta.
I would like to do this by doing the KS test on different
experimental events (no theoretical input), in the asymptotic
limit correlations would show up in deviations from the KS
distribution.

How can you avoid input in generating random output?

However, there are ways of handling this problem.

b) In our field, there are several rather complicated models for
describing particle production.
One can fit a few parameters in these models to describe the
event averages very well. However, this does not mean that these
models are physically sound, as a "proof" very physically
different models fit the same data.

I thought of making a more stringent comparison by KS-testing
a sample of Montecarlo-Generated "events" calculated with these
models (with parameters allready previously determined) together
with experimental events.
This should be more stringent as you are testing not just the
average but the whole distribution (moments/cumulants/...)

What accuracy are you seeking?

At the moment, I am still not sure. I am hoping for a qualitative
answer (are data/model different). An accuracy would than translate
into a confidence level estimate, but
this project is still in a very preliminary stage.

The amount of information is still not enough for
more help than has already been given.

Thanks for the help

GT

If parameters are estimated,
the Monte Carlo generation should be of the same type.

Thanks for the references
GT
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

Relevant Pages

  • Re: Kolmogorov-Smirnov test... a good overview
    ... two samples) do corrections to the KS distribution typically appear? ... "check" of a fit), so my distribution will not have any fit parameters ... momentum of particles in collisions. ... are those of the Statistics Department or of Purdue University. ...
    (sci.stat.math)
  • Re: Kolmogorov-Smirnov test... a good overview
    ... two samples) do corrections to the KS distribution typically appear? ... "check" of a fit), so my distribution will not have any fit parameters ... momentum of particles in collisions. ... are those of the Statistics Department or of Purdue University. ...
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