Extension Fitting

The extension() method executes a source extension analysis for a given source by computing a likelihood ratio test with respect to the no-extension (point-source) hypothesis and a best-fit model for extension. The best-fit 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)

Warning

If the best-fit extension differs significantly from the nominal value, the user is recommended to re-optimize the ROI.

Energy-dependent Extension Fit

Use the option fit_ebin=True to perform separate exention scans in each energy bin (in addition to the joint fit):

gta.extension('sourceA', fit_ebin=True, loge_bins=np.linspace(3, 6.5, 15) )

By default, the method will use the energy bins of the underlying analysis. The loge_bins keyword argument can be used to override the default binning with the restriction that the SED energy bins must align with the analysis bins. The bins used in the analysis can be found with gta.log_energies. For example if in the analysis 8 energy bins per decade are considered and you want to make the SED in 4 bins per decade you can specify loge_bins=gta.log_energies[::2].

User-defined Fit Range

The default extension scan covers 21 points between 0.01 deg and 1.0 deg, evenly spaced in log space. The user may overwrite the fit range (width_min and width_max keywords) and/or the number of points for the scan (width_nstep) or directly supply a list of extensions to be tested (width keyword).

The point source hypothesis is always tested as well. If the extension range includes the nominal extension value used during ROI optimization, this value will be explicitly scanned as well.

Warning

The wider the range of extension values to be fit over, the more important it is to consider freeing the normalization of the background sources to avoid artifacts.

Extension Dictionary

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:

extension Output Dictionary

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	Delta-log-likelihood values for each point in the profile likelihood scan.
loglike	ndarray	Log-likelihood values for each point in the scan over the spatial extension.
loglike_ptsrc	float	Log-Likelihood value of the best-fit point-source model.
loglike_ext	float	Log-Likelihood of the best-fit extended source model.
loglike_init	float	Log-Likelihood of model before extension fit.
loglike_base	float	Log-Likelihood of model after initial spectral fit.
ext	float	Best-fit extension (68% containment radius) (deg).
ext_err_hi	float	Upper (1-sigma) error on the best-fit extension (deg).
ext_err_lo	float	Lower (1-sigma) error on the best-fit extension (deg).
ext_err	float	Symmetric (1-sigma) error on the best-fit extension (deg).
ext_ul95	float	95% CL upper limit on the spatial extension (deg).
ts_ext	float	Test statistic for the extension hypothesis.
ebin_e_min	ndarray
ebin_e_ctr	ndarray
ebin_e_max	ndarray
ebin_ext	ndarray	Best-fit extension as measured in each energy bin (intrinsic 68% containment radius) (deg).
ebin_ext_err	ndarray	Symmetric (1-sigma) error on best-fit extension in each energy bin (deg).
ebin_ext_err_hi	ndarray	Upper (1-sigma) error on best-fit extension in each energy bin (deg).
ebin_ext_err_lo	ndarray	Lower (1-sigma) error on best-fit extension in each energy bin (deg).
ebin_ext_ul95	ndarray	95% CL upper limit on best-fit extension in each energy bin (deg).
ebin_ts_ext	ndarray	Test statistic for extension hypothesis in each energy bin.
ebin_dloglike	ndarray	Delta-log-likelihood values for scan over the spatial extension in each energy bin.
ebin_loglike	ndarray	Log-likelihood values for scan over the spatial extension in each energy bin.
ebin_loglike_ptsrc	ndarray	Log-Likelihood value of the best-fit point-source model in each energy bin.
ebin_loglike_ext	ndarray	Log-Likelihood value of the best-fit extended source model in each energy bin.
ra	float	Right ascension of best-fit position (deg).
dec	float	Declination of best-fit position (deg).
glon	float	Galactic Longitude of best-fit position (deg).
glat	float	Galactic Latitude of best-fit 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	1-sigma 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	1-sigma uncertainty (deg) along major axis of uncertainty ellipse.
pos_err_semiminor	float	1-sigma 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 best-fit 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.

extension Options

Option	Default	Description
fit_ebin	False	Perform a fit for the angular extension in each analysis energy bin.
fit_position	False	Perform a simultaneous fit to the source position and extension.
fix_shape	False	Fix spectral shape parameters of the source of interest. If True then only the normalization parameter will be fit.
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.
make_tsmap	True	Make a TS map for the source of interest.
psf_scale_fn	None	Tuple of two vectors (logE,f) defining an energy-dependent 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.
reoptimize	False	Re-fit ROI in each energy bin. No effect if fit_ebin=False or there are no free parameters
save_model_map	False	Save model counts cubes for the best-fit 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.
tsmap_fitter	tsmap	Set the method for generating the TS map. Valid options are tsmap or tscube.
update	False	Update this source with the best-fit 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 one-dimensional scan of the spatial extension parameter over the range specified with the width parameters. The 1-D profile likelihood is then used to compute the best-fit value, upper limit, and TS for extension. The nuisance parameters that will be simultaneously fit when performing the spatial scan can be controlled with the fix_shape, free_background, and free_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 setting fit_position to True.

Parameters:

• name (str) – Source name.

• loge_bins (ndarray) – Sequence of energies in log10(E/MeV) defining the edges of the energy bins. If this argument is None then the analysis energy bins will be used. The energies in this sequence must align with the bin edges of the underyling analysis instance.

• {options} –

• 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:

dict