Accuracy and error analysis (was Re: [Maxima] primes)
Subject: Accuracy and error analysis (was Re: [Maxima] primes)
From: Stavros Macrakis
Date: Fri, 13 May 2005 12:29:22 -0400
Interval analysis (and the like) is good for giving an upper bound on the
error, but it can be very pessimistic. Besides concentrating on the
extremes, it also assumes that intermediate results aren't correlated.
Consider for example the calculation (a+b)-a where a=[9,11] and b=[2,3].
(a+b) is then [11,14] and [11,14]-a = [11,14]-[9,11] = [0,5]. But the real=20
result range is [2,3].
The all-possible-combinations technique works better in some cases, but
assumes a box-like distribution (whereas most distributions in real life are
much less sharp) and also assumes that the calculation is monotonic in the
inputs. Consider for example a*a for a in [-1,1]: this technique estimates
the resulting range as [1,1], not [0,1]; interval analysis gives [-1,1]!
The simplest technique for estimating a result distribution from input
distributions is Monte Carlo. But it can be computationally expensive....
-s