# TS Map¶

tsmap() generates a test statistic (TS) map for an additional source component centered at each spatial bin in the ROI. The methodology is similar to that of the gttsmap ST application but with the following approximations:

• Evaluation of the likelihood is limited to pixels in the vicinity of the test source position.
• The background model is fixed when fitting the test source amplitude.

TS Cube is a related method that can also be used to generate TS maps as well as cubes (TS vs. position and energy).

For each spatial bin the method calculates the maximum likelihood test statistic given by

$\mathrm{TS} = 2 \sum_{k} \ln L(\mu,\theta|n_{k}) - \ln L(0,\theta|n_{k})$

where the summation index k runs over both spatial and energy bins, μ is the test source normalization parameter, and θ represents the parameters of the background model. The likelihood fitting implementation used by tsmap() only fits the test source normalization (μ). Shape parameters of the test source and parameters of background components are fixed to their current values.

## Examples¶

The spatial and spectral properties of the convolution kernel are defined with the model dictionary argument. The model dictionary format is the same as accepted by add_source().

# Generate TS map for a power-law point source with Index=2.0
model = {'Index' : 2.0, 'SpatialModel' : 'PointSource'}
maps = gta.tsmap('fit1',model=model)

# Generate TS map for a power-law point source with Index=2.0 and
# restricting the analysis to E > 3.16 GeV
model = {'Index' : 2.0, 'SpatialModel' : 'PointSource'}
maps = gta.tsmap('fit1_emin35',model=model,erange=[3.5,None])

# Generate TS maps for a power-law point source with Index=1.5, 2.0, and 2.5
model={'SpatialModel' : 'PointSource'}
maps = []
for index in [1.5,2.0,2.5]:
model['Index'] = index
maps += [gta.tsmap('fit1',model=model)]


The multithread option can be enabled to split the calculation across all available cores:

maps = gta.tsmap('fit1',model=model,multithread=True)


Note that care should be taken when using this option in an environment where the number of cores per process is restricted such as a batch farm.

tsmap() returns a maps dictionary containing Map representations of the TS and predicted counts (NPred) of the best-fit test source at each position.

model = {'Index' : 2.0, 'SpatialModel' : 'PointSource'}
maps = gta.tsmap('fit1',model=model)
print('TS at Pixel (50,50): ',maps['ts'].counts[50,50])


The contents of the output dictionary are given in the following table.

Key Type Description
amplitude Map Best-fit test source amplitude expressed in terms of the spectral prefactor.
npred Map Best-fit test source amplitude expressed in terms of the total model counts (Npred).
ts Map Test source TS (twice the logLike difference between null and alternate hypothese).
sqrt_ts Map Square-root of the test source TS.
file str Path to a FITS file containing the maps (TS, etc.) generated by this method.
src_dict dict Dictionary defining the properties of the test source.

The write_fits and write_npy options can used to write the output to a FITS or numpy file. All output files are prepended with the prefix argument.

Diagnostic plots can be generated by setting make_plots=True or by passing the output dictionary to make_residmap_plots:

maps = gta.tsmap('fit1',model=model, make_plots=True)
gta.plotter.make_tsmap_plots(maps, roi=gta.roi)


This will generate the following plots:

• tsmap_sqrt_ts : Map of sqrt(TS) values. The color map is truncated at 5 sigma with isocontours at 2 sigma intervals indicating values above this threshold.
• tsmap_npred : Map of best-fit source amplitude in counts.
• tsmap_ts_hist : Histogram of TS values for all points in the map. Overplotted is the reference distribution for chi-squared with one degree of freedom (expectation from Chernoff’s theorem).
Sqrt(TS) Map TS Histogram

## Configuration¶

The default configuration of the method is controlled with the tsmap section of the configuration file. The default configuration can be overriden by passing the option as a kwargs argument to the method.

tsmap Options
Option Default Description
exclude None List of sources that will be removed from the model when computing the TS map.
loge_bounds None Restrict the analysis to an energy range (emin,emax) in log10(E/MeV) that is a subset of the analysis energy range. By default the full analysis energy range will be used. If either emin/emax are None then only an upper/lower bound on the energy range wil be applied.
make_plots False Generate diagnostic plots.
max_kernel_radius 3.0 Set the maximum radius of the test source kernel. Using a smaller value will speed up the TS calculation at the loss of accuracy.
model None Dictionary defining the spatial/spectral properties of the test source. If model is None the test source will be a PointSource with an Index 2 power-law spectrum.
multithread False Split the calculation across number of processes set by nthread option.
nthread None Number of processes to create when multithread is True. If None then one process will be created for each available core.
write_fits True Write the output to a FITS file.
write_npy True Write the output dictionary to a numpy file.