estimators - High level estimators

Introduction

The gammapy.estimators submodule contains algorithms and classes for high level flux and significance estimation such as flux maps, flux points, flux profiles and flux light curves. All estimators feature a common API and allow to estimate fluxes in bands of reconstructed energy.

The core of any estimator algorithm is hypothesis testing: a reference model or counts excess is tested against a null hypothesis. From the best fit reference model a flux is derived and a corresponding \(\sqrt{\Delta TS}\) value from the difference in fit statistics to the null hypothesis, assuming one degree of freedom (Estimating Delta TS). In this case \(\sqrt{\Delta TS}\) represents an approximation of the “classical significance”.

In general the flux can be estimated using methods:

1. Based on model fitting: given a (global) best fit model with multiple model components, the flux of the component of interest is re-fitted in the chosen energy, time or spatial region. The new flux is given as a norm with respect to the global reference model. Optionally other component parameters in the global model can be re-optimised.

2. Based on excess: in the case of having one energy bin, neglecting the PSF and not re-optimising other parameters, once can estimate the flux based on excess and derive the significance analytically from the classical Li & Ma solution.

The technical implementation follows the concept of a reference best fit model. Given a global best fit model, the source of interest (for which flux points are computed) is scaled in amplitude by fitting a norm parameter. The fitting is done by grouping the data in time and reconstructed energy bins (reference?).

Based on this algorithm most estimators compute the same basic quantities:

Quantity	Definition
e_ref	Reference energy
e_min	Minimum energy
e_max	Maximum energy
norm	Norm with respect to the reference spectral model
norm_err	Symmetric rrror on the norm derived from the Hessian matrix
ts	Difference in fit statistics (stat_sum - null_value )
sqrt_ts	Square root of TS, corresponds to significance (Wilk’s theorem)

In addition the following optional quantities can be computed:

Quantity	Definition
norm_errp	Positive error of the norm
norm_errn	Negative error of the norm
norm_ul	Upper limit of the norm
norm_scan	Norm scan
stat_scan	Fit statistics scan
stat	Fit statistics value of the best fit model
null_value	Fit statistics value of the null hypothesis

To compute the assymetric errors as well as upper limits one can specify the arguments n_sigma and n_sigma_ul. The n_sigma arguments are translated into a TS value assuming ts = sigma ** 2.

In addition to the norm values a reference spectral model is given. Using this reference spectral model the norm values can be converted to the following different SED types:

Quantity	Definition
dnde	Differential flux at e_ref
flux	Integrated flux between e_min and e_max
eflux	Integrated energy flux between e_min and e_max

The same can be applied for the error and upper limit information. More information can be found on the likelihood SED type page.

Getting Started

An Estimator takes a reduced dataset and model definition as input.

• Flux and significance maps
• Lightcurves

Reference/API

gammapy.estimators Package

Estimators.

Classes

FluxPoints(table)	Flux points container.
LightCurve(table)	Lightcurve container.
ImageProfile(table)	Image profile class.
Estimator	Abstract estimator base class.
ExcessMapEstimator([correlation_radius, …])	Computes correlated excess, sqrt TS (i.e.
TSMapEstimator([model, kernel_width, …])	Compute TS map from a MapDataset using different optimization methods.
ASmoothMapEstimator([scales, kernel, …])	Adaptively smooth counts image.
FluxPointsEstimator([energy_edges, source, …])	Flux points estimator.
LightCurveEstimator([time_intervals, …])	Estimate light curve.
SensitivityEstimator([spectrum, n_sigma, …])	Estimate differential sensitivity.
ImageProfileEstimator([x_edges, method, …])	Estimate profile from image.
ExcessProfileEstimator(regions[, …])	Estimate profile from a DataSet.

Variables

ESTIMATOR_REGISTRY

Registry of estimator classes in Gammapy.