Practical Statistics for the LHC

This document is a pedagogical introduction to statistics for particle physics. Emphasis is placed on the terminology, concepts, and methods being used at the Large Hadron Collider. The document addresses both the statistical tests applied to a model of the data and the modeling itself . I expect to release updated versions of this document in the future.

[1]  J. T. Childers,et al.  Search for the standard model Higgs boson in the diphoton decay channel with 4.9 fb(-1) of pp collision data at √s=7 TeV with ATLAS. , 2012, Physical review letters.

[2]  G. Choudalakis.  Fully Bayesian Unfolding , 2012, 1201.4612.

[3]  Georges Aad,et al.  Search for supersymmetry in final states with jets, missing transverse mome , 2012 .

[4]  Atlas Collaboration.  Search for supersymmetry in final states with jets, missing transverse momentum and one isolated lepton in sqrt{s} = 7 TeV pp collisions using 1 fb-1 of ATLAS data , 2011, 1109.6606.

[5]  R. Cousins.  Negatively Biased Relevant Subsets Induced by the Most-Powerful One-Sided Upper Confidence Limits for a Bounded Physical Parameter , 2011, 1109.2023.

[6]  Bogdan Malaescu,et al.  An Iterative, Dynamically Stabilized (IDS) Method of Data Unfolding , 2011, 1106.3107.

[7]  K. Cranmer,et al.  Power-Constrained Limits , 2011, 1105.3166.

[8]  Tim Adye,et al.  Unfolding algorithms and tests using RooUnfold , 2011, 1105.1160.

[9]  Harrison B. Prosper,et al.  Experience from Searches at the Tevatron , 2011 .

[10]  K. Cranmer,et al.  Asymptotic formulae for likelihood-based tests of new physics , 2010, 1007.1727.

[11]  E. Gross,et al.  Trial factors for the look elsewhere effect in high energy physics , 2010, 1005.1891.

[12]  H. Prosper,et al.  Reference priors for high energy physics , 2010, 1002.1111.

[13]  M. L. Ferrer,et al.  Expected Performance of the ATLAS Experiment - Detector, Trigger and Physics , 2008, 0901.0512.

[14]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[15]  F. Feroz,et al.  MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics , 2008, 0809.3437.

[16]  M. Wolter,et al.  TMVA - Toolkit for Multivariate Data Analysis , 2007, physics/0703039.

[17]  J. Linnemann,et al.  Evaluation of three methods for calculating statistical significance when incorporating a systematic uncertainty into a test of the background-only hypothesis for a Poisson process , 2007, physics/0702156.

[18]  F. Tegenfeldt,et al.  LIKELIHOOD RATIO INTERVALS WITH BAYESIAN TREATMENT OF UNCERTAINTIES: COVERAGE, POWER AND COMBINED EXPERIMENTS , 2005, physics/0511055.

[19]  K. Cranmer.  STATISTICAL CHALLENGES FOR SEARCHES FOR NEW PHYSICS AT THE LHC. , 2005, physics/0511028.

[20]  F. Tegenfeldt,et al.  On Bayesian Treatment of Systematic Uncertainties in Confidence Interval Calculation , 2004, physics/0408039.

[21]  Wolfgang A. Rolke,et al.  Limits and confidence intervals in the presence of nuisance parameters , 2004, physics/0403059.

[22]  G. Punzi.  Comments on Likelihood fits with variable resolution , 2004, physics/0401045.

[23]  G. D'Agostini,et al.  Bayesian inference in processing experimental data: principles and basic applications , 2003, physics/0304102.

[24]  M. Tribus,et al.  Probability theory: the logic of science , 2003 .

[25]  G. Hill.  Comment on `Including systematic uncertainties in confidence interval construction for Poisson statistics' , 2003, physics/0302057.

[26]  A. Read.  Presentation of search results: the CLs technique , 2002 .

[27]  V. Blobel,et al.  An Unfolding Method for High Energy Physics Experiments , 2002, hep-ex/0208022.

[28]  O. Botner,et al.  Coverage Of Confidence Intervals For Poisson Statistics In Presence Of Systematic Uncertainties , 2002, hep-ex/0206034.

[29]  L. Gleser,et al.  Setting confidence intervals for bounded parameters , 2002 .

[30]  O. Botner,et al.  Including systematic uncertainties in confidence interval construction for Poisson statistics , 2002, hep-ex/0202013.

[31]  K. Cranmer,et al.  Kernel estimation in high-energy physics , 2000, hep-ex/0011057.

[32]  A. Read.  Linear interpolation of histograms , 1999 .

[33]  R. Cousins,et al.  A Unified Approach to the Classical Statistical Analysis of Small Signals , 1997, physics/9711021.

[34]  A. Hoecker,et al.  SVD APPROACH TO DATA UNFOLDING , 1995, hep-ph/9509307.

[35]  G. D'Agostini,et al.  A Multidimensional unfolding method based on Bayes' theorem , 1995 .

[36]  R. Cousins.  Why isn’t every physicist a Bayesian? , 1995 .

[37]  Roger Barlow,et al.  Fitting using finite Monte Carlo samples , 1993 .

[38]  J. Q. Smith,et al.  1. Bayesian Statistics 4 , 1993 .

[39]  Robert Cousins,et al.  Incorporating systematic uncertainties into an upper limit , 1992 .

[40]  R. Barlow,et al.  Extended maximum likelihood , 1990 .

[41]  F. James.  Statistical Methods in Experimental Physics , 1973 .

[42]  A. Birnbaum.  On the Foundations of Statistical Inference , 1962 .

[43]  H. Jeffreys.  An invariant form for the prior probability in estimation problems , 1946, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[44]  A. Wald.  Tests of statistical hypotheses concerning several parameters when the number of observations is large , 1943 .

[45]  S. S. Wilks.  The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses , 1938 .

[46]  J. Neyman.  Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability , 1937 .

[47]  K. Pearson.  Biometrika , 1902, The American Naturalist.

[48]  K. Perez.  Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment , 2014 .

[49]  D Casadei.  Reference analysis of the signal + background model in counting experiments , 2012 .

[50]  Procedure for the LHC Higgs boson search combination in Summer 2011 , 2011 .

[51]  Bob Cousins.  Probability Density Functions for Positive Nuisance Parameters , 2010 .

[52]  Michael Woodroofe,et al.  ON THE UNIFIED METHOD WITH NUISANCE PARAMETERS , 2009 .

[53]  Kyle Cranmer,et al.  Statistics for the LHC : Progress, Challenges, and Future , 2008 .

[54]  Luv Demortier,et al.  P Values and Nuisance Parameters , 2008 .

[55]  A. Read.  Modified frequentist analysis of search results (The CL(s) method) , 2000 .

[56]  T. Lai,et al.  Hybrid resampling methods for confidence intervals , 1998 .

[57]  Matts Roos,et al.  MINUIT-a system for function minimization and analysis of the parameter errors and correlations , 1984 .

[58]  F. James,et al.  Errors on ratios of small numbers of events , 1980 .

[59]  O. William.  Journal Of The American Statistical Association V-28 , 1933 .