[ RadSafe ] Stochastic Processes, etc.
JPreisig at aol.com
JPreisig at aol.com
Tue Sep 26 08:49:28 CDT 2006
Hmmmmm,
This is from: jpreisig at aol.com .
Dear Radsafe People:
I hope you are well today. A while back someone on Radsafe was
getting into Stochastic Processes, more for radiation biology/biophysics
than
for something else. Since much of my knowledge on the subject comes
from the fields of geophysics/applied math/EE, I'll just share some
information here (not all of it though, thankfully).
The first thing given here is an approximate quote: The more you
look
at random (stochastic) processes, the less random they become. So, pretty
much as you model your (scientific) deterministic system better and
better,
the more exact (not so random) your whole system becomes (possibly
allowing you to reduce your (statistical) noise levels used in stochastic
modelling).
One means of modelling combined deterministic/stochastic systems
is the Kalman Filter/Smoother. It is especially useful when one has noise
processes like white noise, integrated white noise and similar things. I
don't
know if Kalman Filters are used in radiation biology/biophysics. They
are used
in rocket Guidance Systems. A rocket with a badly designed Kalman
Filter will probably not reach it's target.
I will give some references here, in case you are interested in
reading about
Stochastic Processes and/or Kalman Filtering. A pretty good startup book
is by Robert Grover Brown (Introduction to Random Signal Analysis and
Kalman
Filtering). It also addresses well Kalman Smoothing.
A more mathematical book (quite!!!) is Jazwinski's Stochastic
Processes and
Filtering Theory. It addresses things like Ito Stochastic Calculus and
things like
that. If you can make it past all the theory to the back of the book, you
can find good information on more applied Kalman Filtering. The book also
has a section on linearizing (mildly?) non-linear equations.
If you go to your library, you can find other books on Stochastic
Processes
and Kalman Filtering to fit your needs.
Finally, some information on the word SCALE which has many different
meanings. SCALE is a computer program used for Criticality Calculations
(Ka-Boom!!!!????). A scalar is also a counting device used in Health
Physics.
I'm getting older --- does anyone remember producing a gamma spectrum
using a single channel analyzer??? Thank goodness for the Multi-Channel
Analyzer.
Scaling of parameters is routinely done to produce non-dimensional
parameters. Scaling has a whole different meaning in particle physics
that
I won't get into here. Finally, if one has a matrix with widely varying
(in numerical range) numbers that you want to mathematically invert
directly, you can SCALE that matrix prior to matrix inversion, then invert
the matrix and then UNSCALE (???) the resulting matrix. A book with an
algorithm for doing this was written by Joan Westlake. It's a really neat
book.
So, that's enough for now. I hope this helps someone. The people
in the
guidance system industry can't spill their guts about this stuff (in
detail)
because of their security clearances. Everything discussed here is in
the
public (knowledge) domain. I never have had any security clearance.
(Can't trust German-Americans anyway????!!!!).
You all be good and productive today.
Regards, Joseph R. (Joe) Preisig, Ph.D.
More information about the RadSafe
mailing list