# 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.

## 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([e_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[, e_edges, …]) Estimate profile from a DataSet.

#### Variables¶

 ESTIMATOR_REGISTRY Registry of estimator classes in Gammapy.