Extension Fitting¶
The extension()
method
executes a source extension analysis for a given source by computing a
likelihood ratio test with respect to the noextension (pointsource)
hypothesis and a bestfit model for extension. The bestfit extension
is found by performing a likelihood profile scan over the source width
(68% containment) and fitting for the extension that maximizes the
model likelihood. Currently this method supports two models for
extension: a 2D Gaussian (RadialGaussian) or a 2D disk
(RadialDisk).
At runtime the default settings for the extension analysis can be
overriden by passing one or more kwargs when executing
extension()
:
# Run extension fit of sourceA with default settings
>>> gta.extension('sourceA')
# Override default spatial model
>>> gta.extension('sourceA', spatial_model='RadialDisk')
By default the method will fix all background parameters before
performing the extension fit. One can leave background parameters
free by setting free_background=True
:
# Free a nearby source that maybe be partially degenerate with the
# source of interest. The normalization of SourceB will be refit
# when testing the extension of sourceA
gta.free_norm('sourceB')
gta.extension('sourceA', free_background=True)
# Fix all background parameters when testing the extension
# of sourceA
gta.extension('sourceA', free_background=False)
# Free normalizations of sources within 2 degrees of sourceA
gta.extension('sourceA', free_radius=2.0)
The results of the extension analysis are written to a dictionary which is the return value of the extension method.
ext = gta.extension('sourceA', write_npy=True, write_fits=True)
The contents of the output dictionary are given in the following table:
Key  Type  Description 

name 
str 
Name of source. 
file 
str 
Name of output FITS file. 
config 
dict 
Copy of the input configuration to this method. 
width 
ndarray 
Vector of width (intrinsic 68% containment radius) values (deg). 
dloglike 
ndarray 
Sequence of deltaloglikelihood values for each point in the profile likelihood scan. 
loglike 
ndarray 
Sequence of likelihood values for each point in the scan over the spatial extension. 
loglike_ptsrc 
float 
Model logLikelihood value of the bestfit pointsource model. 
loglike_ext 
float 
Model logLikelihood value of the bestfit extended source model. 
loglike_base 
float 
Model logLikelihood value of the baseline model. 
ext 
float 
Bestfit extension (68% containment radius) (deg). 
ext_err_hi 
float 
Upper (1sigma) error on the bestfit extension (deg). 
ext_err_lo 
float 
Lower (1sigma) error on the bestfit extension (deg). 
ext_err 
float 
Symmetric (1sigma) error on the bestfit extension (deg). 
ext_ul95 
float 
95% CL upper limit on the spatial extension (deg). 
ts_ext 
float 
Test statistic for the extension hypothesis. 
ra 
float 
Right ascension of bestfit position (deg). 
dec 
float 
Declination of bestfit position (deg). 
glon 
float 
Galactic Longitude of bestfit position (deg). 
glat 
float 
Galactic Latitude of bestfit position (deg). 
ra_err 
float 
Std. deviation of positional uncertainty in right ascension (deg). 
dec_err 
float 
Std. deviation of positional uncertainty in declination (deg). 
glon_err 
float 
Std. deviation of positional uncertainty in galactic longitude (deg). 
glat_err 
float 
Std. deviation of positional uncertainty in galactic latitude (deg). 
pos_offset 
float 
Angular offset (deg) between the old and new (localized) source positions. 
pos_err 
float 
1sigma positional uncertainty (deg). 
pos_r68 
float 
68% positional uncertainty (deg). 
pos_r95 
float 
95% positional uncertainty (deg). 
pos_r99 
float 
99% positional uncertainty (deg). 
pos_err_semimajor 
float 
1sigma uncertainty (deg) along major axis of uncertainty ellipse. 
pos_err_semiminor 
float 
1sigma uncertainty (deg) along minor axis of uncertainty ellipse. 
pos_angle 
float 
Position angle of uncertainty ellipse with respect to major axis. 
tsmap 
Map 

ptsrc_tot_map 
Map 

ptsrc_src_map 
Map 

ptsrc_bkg_map 
Map 

ext_tot_map 
Map 

ext_src_map 
Map 

ext_bkg_map 
Map 

source_fit 
dict 
Dictionary with parameters of the bestfit extended source model. 
Configuration¶
The default configuration of the method is controlled with the extension section of the configuration file. The default configuration can be overriden by passing the option as a kwargs argument to the method.
Option  Default  Description 

fit_position 
False  Perform a simultaneous fit to the source position and extension. 
free_background 
False  Leave background parameters free when performing the fit. If True then any parameters that are currently free in the model will be fit simultaneously with the source of interest. 
free_radius 
None  Free normalizations of background sources within this angular distance in degrees from the source of interest. If None then no sources will be freed. 
make_plots 
False  Generate diagnostic plots. 
psf_scale_fn 
None  Tuple of two vectors (logE,f) defining an energydependent PSF scaling function that will be applied when building spatial models for the source of interest. The tuple (logE,f) defines the fractional corrections f at the sequence of energies logE = log10(E/MeV) where f=0 corresponds to no correction. The correction function f(E) is evaluated by linearly interpolating the fractional correction factors f in log(E). The corrected PSF is given by P’(x;E) = P(x/(1+f(E));E) where x is the angular separation. 
save_model_map 
False  Save model counts cubes for the bestfit model of extension. 
spatial_model 
RadialGaussian  Spatial model that will be used to test the sourceextension. The spatial scale parameter of the model will be set such that the 68% containment radius of the model is equal to the width parameter. 
sqrt_ts_threshold 
None  Threshold on sqrt(TS_ext) that will be applied when update is True. If None then nothreshold is applied. 
update 
False  Update this source with the bestfit model for spatial extension if TS_ext > tsext_threshold . 
width 
None  Sequence of values in degrees for the likelihood scan over spatial extension (68% containment radius). If this argument is None then the scan points will be determined from width_min/width_max/width_nstep. 
width_max 
1.0  Maximum value in degrees for the likelihood scan over spatial extent. 
width_min 
0.01  Minimum value in degrees for the likelihood scan over spatial extent. 
width_nstep 
21  Number of scan points between width_min and width_max. Scan points will be spaced evenly on a logarithmic scale between width_min and width_max . 
write_fits 
True  Write the output to a FITS file. 
write_npy 
True  Write the output dictionary to a numpy file. 
Reference/API¶

GTAnalysis.
extension
(name, **kwargs) Test this source for spatial extension with the likelihood ratio method (TS_ext). This method will substitute an extended spatial model for the given source and perform a onedimensional scan of the spatial extension parameter over the range specified with the width parameters. The 1D profile likelihood is then used to compute the bestfit value, upper limit, and TS for extension. The background parameters that will be simultaneously profiled when performing the spatial scan can be controlled with the
free_background
andfree_radius
options. By default the position of the source will be fixed to its current position. A simultaneous fit to position and extension can be performed by settingfit_position
to True.Parameters:  name (str) – Source name.
 fit_ebin (bool) – Perform a fit for the angular extension in each analysis energy bin. (default : False)
 fit_position (bool) – Perform a simultaneous fit to the source position and extension. (default : False)
 free_background (bool) – Leave background parameters free when performing the fit. If True then any parameters that are currently free in the model will be fit simultaneously with the source of interest. (default : False)
 free_radius (float) – Free normalizations of background sources within this angular distance in degrees from the source of interest. If None then no sources will be freed. (default : None)
 make_plots (bool) – Generate diagnostic plots. (default : False)
 psf_scale_fn (tuple) – Tuple of two vectors (logE,f) defining an energydependent PSF scaling function that will be applied when building spatial models for the source of interest. The tuple (logE,f) defines the fractional corrections f at the sequence of energies logE = log10(E/MeV) where f=0 corresponds to no correction. The correction function f(E) is evaluated by linearly interpolating the fractional correction factors f in log(E). The corrected PSF is given by P’(x;E) = P(x/(1+f(E));E) where x is the angular separation. (default : None)
 save_model_map (bool) – Save model counts cubes for the bestfit model of extension. (default : False)
 spatial_model (str) – Spatial model that will be used to test the sourceextension. The spatial scale parameter of the model will be set such that the 68% containment radius of the model is equal to the width parameter. (default : RadialGaussian)
 sqrt_ts_threshold (float) – Threshold on sqrt(TS_ext) that will be applied when
update
is True. If None then nothreshold is applied. (default : None)  update (bool) – Update this source with the bestfit model for spatial
extension if TS_ext >
tsext_threshold
. (default : False)  width (list) – Sequence of values in degrees for the likelihood scan over spatial extension (68% containment radius). If this argument is None then the scan points will be determined from width_min/width_max/width_nstep. (default : None)
 width_max (float) – Maximum value in degrees for the likelihood scan over spatial extent. (default : 1.0)
 width_min (float) – Minimum value in degrees for the likelihood scan over spatial extent. (default : 0.01)
 width_nstep (int) – Number of scan points between width_min and width_max. Scan
points will be spaced evenly on a logarithmic scale between
width_min
andwidth_max
. (default : 21)  write_fits (bool) – Write the output to a FITS file. (default : True)
 write_npy (bool) – Write the output dictionary to a numpy file. (default : True)
 optimizer (dict) – Dictionary that overrides the default optimizer settings.
Returns: extension – Dictionary containing results of the extension analysis. The same dictionary is also saved to the dictionary of this source under ‘extension’.
Return type: