Lectures on Statistics in Theory: Prelude to Statistics in Practice

Abstract

This is a writeup of lectures on "statistics" that have evolved from the initial version for the 2009 Hadron Collider Physics Summer School at CERN to versions for other venues and, most recently, for the African School of Fundamental Physics and Applications in 2024. The emphasis is on foundations, using simple examples to illustrate the points that are still debated in the professional statistics literature. The three main approaches to interval estimation (Neyman confidence, Bayesian, likelihood ratio) are discussed and compared in detail, with and without nuisance parameters. Hypothesis testing is discussed mainly from the frequentist point of view, with pointers to the Bayesian literature. Various foundational issues are emphasized, including the conditionality principle and the likelihood principle.

97 pages, updates for African School of Fundamental Physics and Applications in 2024

References in corpus (22)

• A Unified Approach to the Classical Statistical Analysis of Small Signals
• Confidence Level Computation for Combining Searches with Small Statistics
• Combined Measurement of the Higgs Boson Mass in $pp$ Collisions at $\sqrt{s}=7$ and 8 TeV with the ATLAS and CMS Experiments
• Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC $pp$ collision data at $\sqrt{s}=$ 7 and 8 TeV
• Limits and Confidence Intervals in the Presence of Nuisance Parameters
• Study of the mass and spin-parity of the Higgs boson candidate via its decays to Z boson pairs
• The RooFit toolkit for data modeling
• 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
• The RooStats Project
• A Measurement of $\sin 2\beta$ from $B\to J/\psi K_S^0$ with the CDF detector
• On the Birnbaum Argument for the Strong Likelihood Principle
• Systematic Errors: facts and fictions
• The Search for Neutrino Oscillations numubar->nuebar with KARMEN
• Reference priors for high energy physics
• Discovering the Significance of 5 sigma
• Frequentist Evaluation of Intervals Estimated for a Binomial Parameter and for the Ratio of Poisson Means
• Comment on "Bayesian Analysis of Pentaquark Signals from CLAS Data", with Response to the Reply by Ireland and Protopopsecu
• Comparison of different goodness-of-fit tests
• Raster scan or 2-D approach?
• Negatively Biased Relevant Subsets Induced by the Most-Powerful One-Sided Upper Confidence Limits for a Bounded Physical Parameter
• Combining parameter values or $p$-values
• Testing Hypotheses in Particle Physics: Plots of $p_0$ Versus $p_1$

Cited by in corpus (7)

• Improved constraints on neutrino mixing from the T2K experiment with $3.13\times 10^{21}$ protons on target
• The CMS statistical analysis and combination tool: COMBINE
• Confidence Sets and Hypothesis Testing in a Likelihood-Free Inference Setting
• What is the likelihood function, and how is it used in particle physics?
• Examples of statistical practice in elementary particle physics for comparison with Mayo's severity concept
• Frequentist-Bayes Hybrid Covariance Estimationfor Unfolding Problems
• Comment on "Optimal prior for Bayesian inference in a constrained parameter space" by S. Hannestad and T. Tram, arXiv:1710.08899