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.