Use of maxima in 'statistical engineering'

(apologies if this mail got accidently double posted)
?Hello Richard, 
 
Thanks for your inputs, just tried to download pw.mac on the
verizon.net link you pointed to but the link seems to be down/broken.
Could you just point to an alternative download link if possible?
 
Your point about modeling the pdf by piece wise continous functions is
true and it will work, however a possible concern is that the
computational speed taken with an integration of piece wise functions
may be too long.
 
A secondary minor aspect is how to select the "best" intervals in which
to fit a piece-wise continous function when you just have discrete data
points. Straight polynomials introduce oscillations so cubic and natural
cubic splines are what I normally use. 
 
You can see below for where I was coming from in an earlier message I
sent to Robert if interested (attachments were VRUNC1.mac & VRUNC2.mac) 

 
Best regards,
 
Vishal
 
***************************************************************************************************************************************************
Nice to hear of the work you are involved in.
 
Have a look at the attached to get a qualitative feel for the type of
statistical computations I was more involved last financial year, this
year I am still involved in this but my main focus in the next couple of
months is on a low pressure vacuum design.  
 
I won't send this email to the Maxima mailing list for the moment as it
seems that attachments get scrubbed, so if you think more people who use
Maxima might be interested in this field of statistical computation we
can make a plan to set up FTP access.
 
The slide presentation gives a give overview of the existing approach
and its simplifications and goes on to explain why a Monte Carlo (MC) is
necessary. VRUNC1.mac is for the Guide to Uncertainty Method (GUM) and
VRUNC2.mac is for the MC - just note both should be considered "works in
progress" :)
 
The basic idea is to start with known / assumed statistical information
i.e. probability density functions (pdf's) and to incorporate and
propogate this information through a mathematical model of an instrument
/ system to determine its final statistical state i.e. the pdf either
approximately through the use of the GUM, exactly through solution of
the Markov convolution integral, or numerically using a MC algorithm.
 
The idea can also work 'backwards' by experimentally through
numerical/statistical methods trying to determine what the pdf's for the
inputs are if the final measurand (output) is already known, as a type
of 'inverse problem'.
 
I would appreciate references to the work you are involved in. You can
find more about this field on the National Physical Laboratory (UK)
website in the previous email or in the journal "Metrologia" which is an
IoP publication. 
 
I am aware of the use of inverse Fourier transforms to compute
convolution integrals and have come across it in a conference paper
written by Prof. Maurice Cox who applied it to linear models and
generalized linear models, but I think a straight Monte Carlo method is
more convenient to implement. The use of inverse FFT's can still be used
for validation purposes of more general MC codes.
 
The point to note is that a statistical computational drawing on
symbolic computations will work for algebraic mathematical models of the
system, but cannot easily work for physical systems defined in terms of
partial differential equations (PDE's) unless there is an explicit
closed form solution. Symbolic computations still have a place though
from my perspective in the complete analytical solution of test cases
which can be exactly solved. An example would be certain simple
geometries in which the Navier-Stokes PDE's of fluid mechanics can be
exactly solved and to which the Markov convolution can be usefully
applied such as channel flow in a rectangular duct.
 
Presently I don't have any journal publications but  just some
conference proceedings and various company engineering reports to date.
*************************************************************************************************************************************************************
    ? 

>>> "Richard Hennessy" <rich.hennessy at verizon.net> 8/11/2009 9:31 PM
>>>
Vishal,
 
"using "messy" real life pdf's, which means doing a convolution
integral to get an answer becomes more difficult."
 
Yes but messy functions can be modeled by piecewise continuous
functions and my pw.mac package has some potential here.  I am not sure
if it fits your needs.  I hope it helps.
 
Rich