Determine the confidence region for a model parameter.

**Syntax: ****error**
[[stopat
<ntrial> <toler>] [maximum <redchi>]

[ <delta fit statistic>] [ <model param range>...]]

where

<model param range> =:: [<modelName:>]<first param>-- <last param>

determines the ranges of parameters to be examined, and <delta fit statistic> (distinguished from the model parameter indices by the inclusion of a decimal point), is the change in fit statistic used.

**For response parameters **(see** gain** command),
use **rerror** with identical syntax except:

<response param range> =:: [<sourceNum:>]<first param>-- <last param>

The **error** command uses one of two algorithms. If
Monte Carlo Markov Chains are loaded (see **chain** command) the error range
is determined by sorting the chain values, and then taking a central percentage
of the values corresponding to the confidence level as indicated by <delta fit statistic>.
This is likely to be the faster of the two algorithms.

When chains are **not** loaded, **error**’s algorithm
is as follows:

Each indicated parameter is varied, within its allowed hard
limits, until the value of the fit statistic, minimized by allowing all the
other non-frozen parameters to vary, is equal to the last value of fit statistic
determined by the fit
command plus the indicated <delta
fit statistic>, to within an absolute (not fractional) tolerance of <toler>. Note
that before the **error** command is executed, the data must be fitted. The
initial default values are the range 1—1 and the <delta fit statistic> of 2.706, equivalent
to the 90% confidence region for a single interesting parameter. The number of
trials and the tolerance for determining when the critical fit statistic is
reached can be modified by preceeding them with the stopat keyword. Initially, the values
are 20 trials with a tolerance of 0.01 in fit statistic.

If a new minimum is found in the course of finding the
error, then the calculation is aborted and control returned to the user. The maximum keyword
ensures that **error** will not be run if the reduced chi-squared of the
best fit exceeds <redchi>.
The default value for <redchi>
is 2.0.

Since there are very many scenarios which may cause an **error**
calculation to fail, it is highly recommended that you check the results by
viewing the 9-letter error string, which is part of the output from the **tclout
error** command (see **tclout** for a description of the error string).
If everything went well, the error string should be “FFFFFFFFF”.

Examples:

Assume that the current model has four model parameters.

XSPEC12> error 1-4

//Estimate the 90% confidence ranges for each parameter.

XSPEC12> error 9.0

//Estimate the confidence range for parameters 1-4 with delta fit

// statistic = 9.0, equivalent to the 3 sigma range.

XSPEC12> error 2.706 1 3 1. 2

//Estimate the 90% ranges for parameters 1 and 3, and the 1. sigma

// range for parameter 2.

XSPEC12> error 4

//Estimate the 1. sigma range for parameter 4.

XSPEC12> error stop 20,,3

//Estimate the 1-sigma range for parameter 3 after resetting the number

// of trials to 20.Note that the tolerance field had to be included

//(or at least skipped over).