[ RadSafe ] Stochastic Processes, etc.

[JPreisig at aol.com]

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.