# 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 evaluated by a likelihood profile scan over the source width. Currently this method supports two models for extension: a 2D Gaussian (GaussianSource) or a 2D disk (DiskSource).

The default configuration of extension() is defined in the extension section of the configuration file:

extension Options
Option Default Description
fix_background False Fix any background parameters that are currently free in the model when performing the likelihood scan over extension.
save_model_map False
save_templates False
spatial_model GaussianSource Spatial model use for extension test.
update False Update the source model with the best-fit spatial extension.
width None Parameter vector for scan over spatial extent. If none then the parameter vector will be set from width_min, width_max, and 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 steps for the spatial likelihood scan.

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='DiskSource')


By default the extension method will profile over any background parameters that were free when the method was executed. One can optionally fix all background parameters with the fix_background parameter:

# Free a nearby source that maybe be partially degenerate with the
# source of interest
gta.free_norm('sourceB')

# Normalization of SourceB will be refit when testing the extension
# of sourceA
gta.extension('sourceA')

# Fix all background parameters when testing the extension
# of sourceA
gta.extension('sourceA',fix_background=True)


The results of the extension analysis are written to a dictionary which is the return value of the extension method. This dictionary is also written to the extension dictionary of the corresponding source and will also be saved in the output file generated by write_roi().

ext = gta.extension('sourceA')

ext = gta.roi['sourceA']


The contents of the output dictionary are described in the following table:

extension Output Dictionary
Key Type Description
width ndarray Vector of width values.
dlogLike ndarray Sequence of delta-log-likelihood 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 log-Likelihood value of the best-fit point-source model.
logLike_ext float Model log-Likelihood value of the best-fit extended source model.
logLike_base float Model log-Likelihood value of the baseline model.
ext float Best-fit extension in degrees.
ext_err_hi float Upper (1 sigma) error on the best-fit extension in degrees.
ext_err_lo float Lower (1 sigma) error on the best-fit extension in degrees.
ext_err float Symmetric (1 sigma) error on the best-fit extension in degrees.
ext_ul95 float 95% CL upper limit on the spatial extension in degrees.
ts_ext float Test statistic for the extension hypothesis.
source_fit dict Dictionary with parameters of the best-fit extended source model.
config dict Copy of the input configuration to this method.

## Reference/API¶

GTAnalysis.extension(name, **kwargs)[source]

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. Any background parameters that are free will also be simultaneously profiled in the likelihood scan.

Parameters: name (str) – Source name. spatial_model (str) – Spatial model that will be used when testing extension (e.g. DiskSource, GaussianSource). width_min (float) – Minimum value in degrees for the spatial extension scan. width_max (float) – Maximum value in degrees for the spatial extension scan. width_nstep (int) – Number of scan points between width_min and width_max. Scan points will be spaced evenly on a logarithmic scale between log(width_min) and log(width_max). width (array-like) – Sequence of values in degrees for the spatial extension scan. If this argument is None then the scan points will be determined from width_min/width_max/width_nstep. fix_background (bool) – Fix all background sources when performing the extension fit. update (bool) – Update this source with the best-fit model for spatial extension. save_model_map (bool) – Save model maps for all steps in the likelihood scan. extension – Dictionary containing results of the extension analysis. The same dictionary is also saved to the dictionary of this source under ‘extension’. dict