In the theory of statistics, one can show that in the asymptotic llmit, any of several methods of determining parameter errors are equivalent and will give the same result. Let us for the moment call these methods [MIGrad]MIGRAD, [HESse]HESSE, and [MINos]MINOS ([SIMplex]SIMPLEX is a special case). It turns out that the conditlons under which these methods yield exactly the same errors are either of the following:
It may happen that (1) is satisfied, in whlch case you don't really
need Minuit, a smaller, simpler, and faster program would do, since
a linear problem can be solved directly without iterations (see [5],
p. 163-165), for example with CERN library program LSQQR.
Nevertheless, it may be convenient to use Minuit slnce non-linear
terms can then be added later if desired, without major changes to
the method. Condition (2) is of course never satisfied, although in
practice it often happens that there is enough data to make the
problem ``almost linear'', that is there is so much data that the
range of parameters allowed by the data becomes very small, and
any physical function behaves linearly over a small enough region.
The following sections explain the dirrerences between the various parameter errors given by Minuit.