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method
change the fitting method
Set the minimization method.
| Syntax: | method | <algorithm>[<# of trials/evaluations>[<method-specific options>]] |
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where <algorithm> is the method in use and the other arguments are
control values for the minimization. Their meanings are explained under the
individual methods. The migrad and simplex methods are taken
from the CERN Minuit2 package, with documentation located at
http://seal.web.cern.ch/seal/MathLibs/Minuit2/html/index.html. If either of
these are used, then the error command will use the Minuit2 minos
method to find the confidence regions.
| Syntax: | method | leven [<# of eval>] [<crit delta>] [<crit beta>]] [delay |nodelay] |
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The default XSPEC minimization method using the modified Levenberg-Marquardt algorithm based on the CURFIT routine from Bevington. <# of eval> is the number of trial vectors before the user is prompted to say whether they want to continue fitting. <crit delta> is the convergence criterion, which is the (absolute, not fractional) difference in fit statistic between successive iterations, less than which the fit is determined to have converged.
<crit beta> refers to the |beta|/N value reported during a fit. This is the norm of the vector of derivatives of the statistic with respect to the parameters divided by the number of parameters. At the best fit this should be zero, and so provides another measure of how well the fit is converging. When this is set to a positive value, it will provide another fit stopping criterion in addition to that of the <crit delta> setting.
Including the string delay as an argument turns on delayed gratification. It is turned off by nodelay. Delayed gratification modifies the way the damping parameter is set and has been shown in many cases to speed up convergence. The default is nodelay.
<# of eval>, <crit delta>, <crit beta>, delay, and nodelay may also be set through the fit command.
This method requires the first derivatives of the statistic with respect to the parameters, and an estimate of the second derivatives. When every component of the active models has a registered analytic gradient, the first derivatives are by default computed analytically in a single pass (Appendix H); set xset DISABLE_ANALYTIC_GRAD yes to revert to finite differences (for example to reproduce fit paths from earlier versions). The second derivatives are by default estimated using an analytic expression which assumes that partial 2nd derivatives of the model with respect to its parameters may be ignored. This may be changed with xset usechainrule no (or by setting the USE_CHAIN_RULE flag to false in the user's startup Xspec.init initialization file); XSPEC will then differentiate the statistic numerically, which can be noticeably slower.
| Syntax: | method | migrad [<# of eval>] [<minuit strategy>] [<minuit tolerance>] |
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The Minuit2 migrad method. <# of eval> is the number of function evaluations to perform before giving up. Migrad uses an internal convergence criterion. <minuit strategy> takes values 0, 1, or 2 with 0 the fastest method but with lowest reliability and 2 the slowest method with highest reliability. The default is 2. The fit will stop when the estimated difference between the current fit statistic and the minimum is less than <minuit tolerance> times 0.001. The default tolerance is 0.1.
The current version of Minuit2 included is that from ROOT v5.34. Documentation on Minuit2 can be found at http://seal.web.cern.ch/seal/MathLibs/Minuit2/html/.
Parameter limits and the Minuit methods. Both Minuit methods work in
the parameter's value directly, and soft limits have no effect on them.
Where a hard limit is passed to Minuit, Minuit enforces it by minimizing in an
internal coordinate of its own: for a parameter bounded on both sides the
external value 
is related to the internal one
by
The cost is resolution. The internal coordinate covers the whole allowed range over an interval of order unity, so the wider the range between the hard limits, the less of the external parameter each internal step can resolve. A range far wider than the region the parameter can plausibly occupy therefore degrades the minimization and, more visibly, the uncertainties Minuit reports from its error matrix. This is Minuit's own advice as well: do not use limits you do not need, and where you do need them, make them tight.
XSPEC passes a parameter's hard limits to Minuit only when they span a range of
100 or less; a parameter whose hard limits are wider than that – which
includes every normalization, whose default hard maximum is 
– is
given to Minuit unbounded. Such a parameter is still confined to its hard
limits, because XSPEC clamps it there, but outside them Minuit sees a flat
statistic rather than a boundary.
The practical advice when fitting with migrad or simplex is
therefore to set the hard limits of the free parameters explicitly, with
newpar, to a range the parameter can plausibly take – for a
normalization known to within a few orders of magnitude, say, a range of 
rather than – and to check afterwards that no parameter has ended up
against a limit you imposed. Soft limits will not restrain a Minuit fit, and
the reported uncertainties are only as good as the range Minuit was given.
If migrad is still not working well, try fit global or a different starting point; a fit that reports convergence with a parameter pegged at a limit has usually not converged at all.
A Minuit fit can end short of the minimum in two ways, and neither is visible in the parameter values it leaves behind, so XSPEC reports both. The test in each case is the estimated distance to the minimum (edm) — Minuit's own estimate of how far in fit statistic the current point is from the minimum — against the criterion Minuit converges on, which is 0.002 times the tolerance.
The first is running out of function evaluations. This is ordinary, and continuing is simply another fit:
***Warning: migrad stopped at its limit on function evaluations, with an estimated distance to the minimum of 1.86779 against a convergence criterion of 0.0002. It has not converged. Fit again to continue from this point, or raise the number of evaluations in the method command.The second is Minuit stopping of its own accord, when the error matrix it carries between iterations yields no direction of improvement. Fitting again from that point will do the same thing, so the remedy is different:
***Warning: migrad did not converge. Minuit found no direction of improvement from this point, with an estimated distance to the minimum of 3306.74 against a convergence criterion of 0.0002. The parameter values below are where it stopped and may not be the minimum.A fit that ends either way has not been minimized to Minuit's own satisfaction, whatever the parameter values look like. Note that the edm is an estimate made from the error matrix, so a fit that has in fact reached the minimum can still report a value above the criterion; what the warning tells you is that Minuit stopped for a reason other than convergence.
| Syntax: | method | simplex [<# of evaluations>] [<minuit strategy>] [<minuit tolerance>] |
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The Minuit2 simplex method. <# of evaluations>is the number of function evaluations to perform before giving up. Simplex uses an internal convergence criterion. <minuit strategy> takes values 0, 1, or 2 with 0 the fastest method but with lowest reliability and 2 the slowest method with highest reliability. The default is 2. The fit will stop when the estimated difference between the current fit statistic and the minimum is less than <minuit tolerance> times 0.001. The default tolerance is 0.1.
This method is included for historical interest and is almost always outperformed by migrad.
| Syntax: | method | global [<maxgen>[<popsize>]] |
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The derivative-free Differential Evolution (DE) global optimizer. Unlike
leven, migrad, and simplex — which are
local optimizers that descend to the nearest minimum from the current
parameter values — global searches the full soft-limit
(“min”/“max”) box of every thawed parameter using only statistic
evaluations, so it can cross barriers between local minima and works for the
entire model library, including local models that provide no analytic
gradients. <maxgen> sets the number of DE generations (default 200)
and <popsize> the population size (default automatic,
for 
thawed parameters, and never fewer
than 4); these are the only tunable controls. The search is reproducible
under xset seed, and its likelihood batch can be spread over 
processes with parallel global <N>.
In most cases you do not select this method directly. The recommended way to use the global search is the fit global command, which runs a DE sweep as a preconditioner and then polishes the best point it finds with your local method (leven, migrad, or simplex) — combining DE's global reach with a local optimizer's accurate final statistic, parameter errors, and covariance, and adding never-regress protection and competitive-basin reporting. Selecting method global instead makes every subsequent fit a bare DE search with no local polish, which is coarser and rarely what you want. improve is the warm-restart form of the same DE machinery. See fit global for a full description of the global search, its behaviour on wide-range parameters, and its output.