This unit covers proper error calculation including (auto-)correlation effects for primary and derived observables and discusses solutions for most common fitting problems, with emphasis on data from MC (→ correlations). Much of the statististical and numerical analysis is well covered in textbooks and reviews, so the core material is concise and provides guidance into the literature. Advanced methods such as Gamma method are covered in more detail.
Units: Essentials, Algorithms , basic working knowledge of fundamentals of statistics.
Definitions
Moments, mean, variance, skewness, kurtosis, . . . Random samples and estimators
Law of large numbers, central limit theorem 0.2
Normal distribution and statistical errors
Error propagation
Pseudo Random numbers
Monte Carlo integration
Binning
Jackknife binning
Bootstrap
Γ−method
Linear least squares
Bayesian Fits
Maximum Entropy Methods
Data Analysis in High Energy Physics: A Practical Guide to Statistical Methods [various authors, Viley-vch]
Mathematical Methods for Physics and Engineering [K.F.Riley, M.P.Hobson, S.J.Bence, Cambridge University Press]
Algorithms for Dynamical Fermions [A.D.Kennedy, arXiv:hep-lat/0607038]
(First chapter gives a very lattice-centered introduction to PDFs)
UWerr [Ulli Wolff, Comput.Phys.Commun. 156 (2004)]
Automatic windowing and errors of errors. originally in MATLAB/octave but has been ported to python, julia, R, . . .
pyobs [Mattia Bruno]
Written in python, projected observables
aderrors [Alberto Ramos, Comput.Phys.Commun. 238 (2019)]
Projected observables, automatic differentiation for ∂f/∂Aα, versions in FORTRAN and Julia
pyerrors [F.Joswig, S.Kuberski, J.Kuhlmann, J.Neuendorf, arXiv:2209.14371]
Very well documented, similar features as aderrors, written in python
Numerical Recipes [W.H.Press, S.A.Teukolsky, W.T.Vetterling, B.P.Flannery]
Matrix Computations [G.H.Golub, C.F.Van Loan]
Computational Strategies in Lattice QCD [M.Lüscher, arXiv:1002.4232]