The Linear Template Fit

TL;DR

The paper introduces the Linear Template Fit, an analytic solution for simulation-based parameter estimation that combines linear regression and least squares, optimized for performance-critical and computationally intensive applications.

Contribution

It presents the Linear Template Fit method, providing a closed-form analytic solution for parameter estimation in simulation-based problems, including error propagation and a nonlinear extension.

Findings

Efficient parameter estimation with minimal simulations

Closed-form error propagation equations

Application to LHC jet cross section data

Abstract

The estimation of parameters from data is a common problem in many areas of the physical sciences, and frequently used algorithms rely on sets of simulated data which are fit to data. In this article, an analytic solution for simulation-based parameter estimation problems is presented. The matrix formalism, termed the Linear Template Fit, calculates the best estimators for the parameters of interest. It combines a linear regression with the method of least squares. The algorithm uses only predictions calculated for a few values of the parameters of interest, which have been made available prior to its execution. The Linear Template Fit is particularly suited for performance critical applications and parameter estimation problems with computationally intense simulations, which are otherwise often limited in their usability for statistical inference. Equations for error propagation are discussed in detail and are given in closed analytic form. For the solution of problems with a nonlinear dependence on the parameters of interest, the Quadratic Template Fit is introduced. As an example application, a determination of the strong coupling constant from inclusive jet cross section data at the CERN Large Hadron Collider is studied and compared with previously published results.