3.1.26. Simulate: Simulation of data

3.1.26.1. Overview

This command is used for spectral simulations. The user should start with a spectral model and a spectral data set (both matrix and spectrum). After giving the “simulate” command, the observed spectrum will be replaced by the simulated spectrum in SPEX. Note that the original spectrum file (with the .spo extension) is not overwritten by this command, so no fear to destroy your input data!

Different options exist and several parameters can be set:

  • Instrument, region: the instrument(s) and region(s) for which the simulation should be done (i.e., if you have more instruments you can do the simulation only for one or a few instruments).

  • time: set the exposure time t (s) of the source spectrum as well as the background error scale factor f_b. This last option allows you to see what happens if for example the background would have a ten times higher accuracy (for f_b=0.1).

  • syserr: add a systematic error to both the source and background spectrum. An alternative way to introduce systematic errors is of course to use the syserr command (Syserr: systematic errors). Take care not to set the systematic errors twice, and remember that rebinning your spectrum later will reduce the systematic errors, as these will be added in quadrature to the statistical errors. So first rebin and then add systematics!

  • noise: either randomize your data or just calculate the expected values.

  • bnoise: randomize your background model (generally not recommended to do).

  • seed: set the random seed either to a specific number or generate it from the system clock. By default, SPEX initializes the random number generator based on the system clock, but through this command a specific seed can be set. The command will show the seeds used for the maximum number of expected threads.

Warning

A response matrix and spectrum of the region and the instrument you want to simulate are necessary, because SPEX needs the response matrix as well as the background to be subtracted for the simulations.

Warning

When you include systematic errors in the simulation (by putting the “syserr” to non-zero values), you cannot use anymore Poissonian statistics hence the C-stat for fitting, but you have to use the “fit meth chi” to use Gaussian errors and \chi^2-fitting, with all thr disadvantages of that.

Warning

When you use bnoise=true, your subtracted background (the scaled background from the background region) will be randomized, and the pure C-stat cannot be used; the W-stat can be used as alternative but has serious drawbacks and is not recommended to be used).

Warning

(obsolete) If your background is taken from the same observation as your source, and you multiply the original exposure time with a factor of S, you should put f_b to S^{-0.5}, reflecting the fact that with increasing source statistics the background statistics also improves. This is the case for an imaging observation where a part of the image is used to determine the background. If instead you use a deep field to subtract the background, then the exposure time of your background will probably not change and you can safely put f_b=1 for any exposure time t.

Warning

(obsolete) If your subtracted background (one of the columns in the .spo file) is derived from a low statistics Poissonian variable (for example a measured count rate with few counts per channel), then scaling the background is slightly inaccurate as it takes the observed instead of expected number of background counts as the starting point for the simulation.

3.1.26.2. Syntax

Note that only the “simulate” keyword followed by a number (the exposure time will do the actual simulation. All other syntax rules just set some parameters. The following syntax rules apply:

simulate #r : Does the simulation, with #r the exposure time t in seconds.
simulate instrument #i1 : Specify the instrument (range) to be used in the simulation. Default values are 1 (just the first instrument).
simulate region #i1 : Specify the region (range) to be used in the simulation. Default values are 1 (just the first region). For simulating everything you have, you can put this range to a large value: the simulation will simply ignore non-existent regions. If you use complex settings, like only region 3 for instrument 1 and region 2 for instrument 2, you may have to run the simulation separately for each entity.
simulate syserr #r1 #r2 : Specify the systematic errors as a fraction of the source and background spectrum, respectively; both should be specified together. Default values are 0.
simulate noise #l : If #l is true, Poissonian noise will be added (this is the default).
simulate bnoise #l : If #l is false, no Poissonian noise will be added to the model background (this is the default).
simulate seed #i : Set random seed to a particular number.
simulate seed random : Set random seed randomly based on system clock.

3.1.26.3. Examples

simulate 10000. : This simulates a new spectrum/dataset with 10 000 s exposure time.
simulate noise f : Set simulation flag to simulate without Poissonian noise. The nominal error bars will still plotted.
simulate syserr 0.1 0.2 : Set simulation for a systematic error of 10 % of the source spectrum and 20 % of the subtracted background spectrum added in quadrature.
simulate instrument 2:4 : Set simulation for a spectrum for instruments 2–4 only
simulate region 2 : Set simulation for only region 2 (of every instrument involved
simulate seed 2 : Set random number seed to 2.