We have retained this Monte Carlo search mainly for sentimental reasons, even though the limited experience with it is less than spectacular. The method now incorporates a Metropolis algorithm which always moves the search region to be centred at a new minimum, and has probability
of moving the search region to a higher point with function value F. This gives it the theoretical ability to jump through function barriers like a multidimensional quantum mechanical tunneler in search of isolated minima, but it is widely believed by at least half of the authors of Minuit that this is unlikely to work in practice (counterexamples are welcome) since it seems to depend critically on choosing the right average step size for the random jumps, and if you knew that, you wouldn't need Minuit.
4cmSIMPLEX
This genuine multidimensional minimization routine is usually much
slower than [MIGrad]MIGRAD, but it does not use first derivatives,
so it should not be so sensitive to the precision of the FCN
calculations, and is even rather robust with respect to
gross fluctuations in the function value.
However, it gives no reliable information about parameter errors,
no information whatsoever about parameter correlations,
and worst of all cannot be expected to converge accurately
to the minimum in a finite time.
Its estimate of EDM is largely fantasy, so it would not even
know if it did converge.
4cmFloating point Precision
Minuit figures out at execution time the precision with which it was compiled, and assumes that FCN provides about the same precision. That means not just the length of the numbers used and returned by FCN, but the actual mathematical accuracy of the calculations. The section on Floating point Precision in Chapter One describes what to do if this is not the case.