[R] Inference for R Spam

Michael A. Miller mmiller3 at iupui.edu
Thu Mar 5 18:44:49 CET 2009


>>>>> "Rolf" == Rolf Turner <r.turner at auckland.ac.nz> writes:

    > My impression --- and I could be wrong --- is that
    > physicists understanding of randomness is very narrow and
    > constrained.  They tend to think along the lines of chaotic
    > dynamical systems (although perhaps not consciously; and
    > they may not explicitly express themselves in this way).
    > They also tend to think exclusively in terms of measurement
    > error as the source of variability.  Which may be
    > appropriate in the applications with which they are
    > concerned, but is pretty limited.  Also they're a rather
    > arrogant bunch.  E.g.  Rutherford (???): ``If I need
    > statistics to analyze my data I need more data.''


This is an interesting discussion all around, but as one of those
physicists I feel a need to jump back in ;-) Just as in any
multidisciplinary endeavor, much of the fun comes from bridging
communication gaps that arise from our certainty that "everyone
knows" what we mean when we say what we say.

First, I counter with a quote from my list of interesting sayings :-)

 "We must be careful not to confuse data with the abstractions
  we use to analyze them."  --- William James

I went through an interesting transition when I moved from basic
physics (medium energy nuclear/particle physics) to biomedical
applications (cardiology and then imaging sciences/radiology).
There is an important difference between physics-y statistical
analysis and biomedical-y statistical analysis that I was not
aware of before I crossed over to the biomedical side.  That my
biomedical and biostatisticians colleagues didn't have the same
background didn't make their perspective invalid, just as my not
having a background in biomedical statistics didn't make me
arrogant.  That we were unaware that we were sometimes speaking
different languages made up of the same words lead to some
adventures.

I had to learn two things.  One, that biomedical systems tend to
have broad distributions while many physical systems have very
narrow distributions.  Two, that physics models are based on
physics theories and that biomedical/biostats models are purely
phenomonological and only model the data - they often do not have
a basis in underlying physical theory.  Simple, but not stressed
in my statistical physics or biomedical statistics training.

Perhaps the key example is statistical mechanics, both classical
and quantum mechanical.  A fundamental physics-y concept is that
a single object has no statistical properties.  "Statistical" is
a word reserved for properties of ensembles.  Statistical
mechanics can only be applied to ensembles of objects where their
joint behavior leads to (highly) predictable results.  The
density of states for any macroscopic ensemble of like objects is
extremely sharply peaked, leading to wonderfully reliable
theoretical predictions.  Just the opposite of what we tend to
see in biomedical systems.

For those who are interested in a physics-y perspective, I'd
suggest taking a crack at "Statistical Methods in Experimental
Physics" (F. James) and some of the many statistical mechanics
texts out there.  My favorites are still F. Mandl's "Statistical
Physics" and K. Huang's "Statistical Mechanics," but there are
many, many more.

Another nice little book is "Observational Foundations of
Physics" by Cook.  It addresses in part the question of why
mathematics is so startlingly effective in physics.  It is a
result of the correspondence between physical processes in the
natural world and mathematical groups.  As far as I know, a
similar correspondence does not exist in the biomedical realm,
nor in many other domains.  That lack of correspondence leads to
purely phenomonological models that model the data but are not
based on underlying physical theory - all that is left is
statistical modeling.  I suspect this is the source of the sort
of statement you attributed to Rutherford.  I hear him simply
saying that we can do perfectly respectable statistical modeling
without physics, but then it is not physics.  And if our goal is
to do physics, then we aught to get back to the lab and observe
reality some more.  Which is where the fun is for many of us
scientists!

Regards, Mike

-- 
Michael A. Miller                             mmiller3 at iupui.edu
  Department of Radiology, Indiana University School of Medicine




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