ÒÉthe very gameÉÓ
A Tutorial on Mathematical Modeling
Michael P. McLaughlin
/~mikemclaughlin
© Dr. Michael P. McLaughlin
1993-1999
This tutorial is distributed free of charge and may neither be sold nor repackaged for sale in
whole or in part.
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ii
PREFACE
“OK, I’ve got some data. Now what?”
It is the quintessence of science, engineering, and numerous other disciplines to make
quantitative observations, record them, and then try to make some sense out of the resulting
dataset. Quite often, the latter is an easy task, due either to practiced familiarity with the
domain or to the fact that the goals of the exercise are undemanding. However, when working
at the frontiers of knowledge, this is not the case. Here, one encounters unknown territory,
with maps that are sometimes poorly defined and always plete.
The question posed above is nontrivial; the path from observation to understanding is, in
general, long and arduous. There are techniques to facilitate the journey but these are seldom
taught to those who need them most. My own observations, over the past twenty years, have
disclosed that, if a functional relationship is nonlinear, or a probability distribution something
other than Gaussian, Exponential, or Uniform, then analysts (those who are not statisticians)
are usually unable to cope. As a result, approximations are made and reports delivered
containing conclusions that are urate and/or misleading.
With scientific papers, there are always peers who are ready and willing to second-guess
any published analysis. Unfortunately, there are as well many less mature disciplines which
lack the checks and balances that science has developed over the centuries and which frequently
address areas of public concern. These concerns lead, inevitably, to public decisions and
warrant the best that mathematics and statistics have to offer, indeed, the best that analysts can
provide. Since Nat
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