Accuracy and error analysis (was Re: [Maxima] primes)

C Y (smustudent1@yahoo.com) wrote:

> One of the longer term ideas I have for units and physics
> pacakges in general is a way to do intelligent error propagation, 
> incorporating user defined uncertainties and if possible the 
> uncertainty in Maxima's calculations as well.

There is a great practical need for analysis of uncertainty
in calculated results, not in the sense of microscopic
round-off error but in the sense of uncertainty attached
to macroscopic quantities.

The right way to approach this (IMHO) is to consider this
as an exercise in Bayesian statistics: assign probability
distributions to everything in sight, then turn the crank
a few times to find the posterior distribution of whatever
you're after. This is generally somewhere between onerous
and impossible, but, given its practical importance, still
worth attempting.

> I guess the ideal thing would be for all variables in
> Maxima to be treated as objects, with one of the available
> pieces of information being an uncertainty that reflects the
> history of the value within Maxima, but I have no idea how
> practical that is.

Careful propagation of uncertainty would entail a very
pervasive revision of the existing code. A different 
approach would be to construct another program which, 
given a programming function, would propagate uncertainty 
through it. This is probably more nearly feasible in 
Maxima and/or Lisp than in other programming languages.

For what it's worth,
Robert Dodier


		
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