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error, uncertain: determine confidence intervals of a fit

Determine the confidence region for a model parameter.

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

[ <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, the default behavior is to abort the calculation and then automatically rerun it using the new best fit parameters. If you prefer not to automatically rerun the error calculation, then enter nonew at the start of the command string. 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 nonew 4

//Same as before, but calculation will NOT automatically restart if a new minimum is found.

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).

 

next up previous contents
Next: fit Up: Fit Commands Previous: chain