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.Comment: presented at the 2011 European School of High-Energy Physics, Cheile Gradistei, Romania, 7-20 September 2011 I expect to release updated versions of this document in the futur

Statistical Challenges for Searches for New Physics at the LHC

Because the emphasis of the LHC is on 5 sigma discoveries and the LHC environment induces high systematic errors, many of the common statistical procedures used in High Energy Physics are not adequate. I review the basic ingredients of LHC searches, the sources of systematics, and the performance of several methods. Finally, I indicate the methods that seem most promising for the LHC and areas that are in need of further study.Comment: 12 pages, 7 figures, proceedings of PhyStat2005, Oxford. To be published by Imperial College Press. See http://www.physics.ox.ac.uk/phystat05/index.ht

Frequentist Hypothesis Testing with Background Uncertainty

We consider the standard Neyman-Pearson hypothesis test of a signal-plus-background hypothesis and background-only hypothesis in the presence of uncertainty on the background-only prediction. Surprisingly, this problem has not been addressed in the recent conferences on statistical techniques in high-energy physics -- although the its confidence-interval equivalent has been. We discuss the issues of power, similar tests, coverage, and ordering rules. The method presented is compared to the Cousins-Highland technique, the ratio of Poisson means, and ``profile'' method.Comment: Talk from PhyStat2003, Stanford, Ca, USA, September 2003, 4 pages, LaTeX, 2 eps figures. PSN WEMT00

Potential for Higgs Physics at the LHC and Super-LHC

The expected sensitivity of the LHC experiments to the discovery of the Higgs boson and the measurement of its properties is presented in the context of both the standard model and the its minimal supersymmetric extension. Prospects for a luminosity-upgraded ``Super-LHC'' are also presented.Comment: Invited talk at 2005 International Linear Collider Physics and Detector Workshop and Second ILC Accelerator Workshop, Snowmass, CO(Snowmass05) 3 pages, 0 figures. PSN ALCPG060

Multivariate Analysis from a Statistical Point of View

Multivariate Analysis is an increasingly common tool in experimental high energy physics; however, many of the common approaches were borrowed from other fields. We clarify what the goal of a multivariate algorithm should be for the search for a new particle and compare different approaches. We also translate the Neyman-Pearson theory into the language of statistical learning theory.Comment: Talk from PhyStat2003, Stanford, Ca, USA, September 2003, 4 pages, LaTeX, 1 eps figures. PSN WEJT00

Adversarial Variational Optimization of Non-Differentiable Simulators

Complex computer simulators are increasingly used across fields of science as generative models tying parameters of an underlying theory to experimental observations. Inference in this setup is often difficult, as simulators rarely admit a tractable density or likelihood function. We introduce Adversarial Variational Optimization (AVO), a likelihood-free inference algorithm for fitting a non-differentiable generative model incorporating ideas from generative adversarial networks, variational optimization and empirical Bayes. We adapt the training procedure of generative adversarial networks by replacing the differentiable generative network with a domain-specific simulator. We solve the resulting non-differentiable minimax problem by minimizing variational upper bounds of the two adversarial objectives. Effectively, the procedure results in learning a proposal distribution over simulator parameters, such that the JS divergence between the marginal distribution of the synthetic data and the empirical distribution of observed data is minimized. We evaluate and compare the method with simulators producing both discrete and continuous data.Comment: v4: Final version published at AISTATS 2019; v5: Fixed typo in Eqn 1