In order to provide for full generality in the user-defined function
value, the user is allowed to define a normalization factor known
internally as UP and defined by the Minuit user on an
[SET ERRordef]ERROR DEF command card.
The default value is one. The Minuit error on a
parameter is defined as the change of parameter which would
produce a change of the function value equal to UP.
This is the most
general way to define the error, although in statistics it is more
usual to define it in terms of the second derivative of the
function -- with respect to the parameter in question. In the
simplest linear case (when the function is exactly parabolic at the
minimum), the value UP=1.0 corresponds to defining the error as the
inverse of the second derivative at the minimum. The fact that
Minuit defines the error in terms of a function change does not mean
that it always calculates such a function change. Indeed it
sometimes ([HESse]HESSE) calculates the second derivative matrix and
inverts it, assuming a parabolic behaviour. This distinction is
discussed in section 
.
The purpose of defining errors by function changes is threefold:
);
).