Loving ISIS - Confessions of a Former XSPEC User

Systematic Errors and Custom Statistics:

ISIS allows a fair amount of flexibility over the way statistics are calculated and errors are propagated. As in XSPEC, you don't have to think about this if you don't want to, but if you do want to, there's several choices that you can make:

You can decide what minimization method to use. This is discussed more here.
You can decide what fit statistic to minimize: chi squared, cash, or a user defined statistic.
For the chi squared statistic, you can decide which measure of the variance you use: taken from the data, the gehrels error calculated from the binned counts, taken from the model counts, a uniform variance of 1 (lsq), or a user defined error statistic.
The default statistic is chi squared, with a variance defined to be the binned data counts (i.e., the error being square root of binned counts -- simple Poisson statistics). However, you can redefine how errors are propagated for a rebinned dataset.

Some of the ISIS intrinsic functions designed to allow you to make these choices are:

     set_fit_method("choice");                 %  Choose minimization method ...
     load_fit_method("library.so","name");     %  ... or create your own
     set_fit_statistic("choice");              %  Choose chi squared or cash ...
     load_fit_statistic("library.so","name");  %  ... or create your own
     set_rebin_error_hook(id,"name");          %  Propagate errors your own way

Most people most of the time seem to be happy with chi squared statistics with error bars defined by Poisson statistics in each data bin (i.e., the ISIS and XSPEC defaults). In this example, a notable exception is for the high count rate PCA statistics, which are dominated by systematic uncertainties.

As there are no truly universally accepted and proper ways of dealing with systematic errors, and consistent with its philosophy of expecting you to do all binning during analysis, ISIS will ignore any systematic error flags placed in the FITS file headers. I.e., it forces you to make a conscious choice about what to do with systematic errors.

For those that don't want to worry about that conscious choice, I have created a function:

set_systematics(id,[lo],[hi],[err]);

which will apply fractional systematic errors in much the "usual" way (i.e., by adding systematic errors in quadrature to the data errors), and will still allow you to actively rebin datasets during an ISIS analysis session. (The function uses the set_rebin_error_hook() function.) The [lo] and [hi] channel numbers refer to unbinned channel numbers, and are in wavelength/energy space, depending upon whether the global variable (created and defined by my .isisrc) Isis_Reverse_Channels=0/1, respectively. (The latter choice is the default in my .isisrc.)

Important Note: ISIS does set a lower bound to the minimum size of a statistical error bar (to avoid roundoff errors, etc.). We violate this lower bound when defining the radio data as a counts/bin dataset. Thus, we overwrite that choice in my .isisrc files by setting:

     Minimum_Stat_Err = 1.e-30;

On the next page, we take a brief digression to discuss model grids.

This page was last updated Mar 22, 2006 by Michael Nowak. To comment on it or the material presented here, send email to mnowak@space.mit.edu.