Misc,
The Linear Template Fit
(2021)cite arxiv:2112.01548Comment: 47 pages, 11 figures, 3 tables, including minor changes during journal review.
DOI: 10.1140/epjc/s10052-022-10581-w
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.
