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Comment on Frank Porter, "Confidence intervals for the Poisson distribution"
Robert D. Cousins
Frank Porter has recently posted a review of "Confidence intervals for the Poisson distribution" (arXiv:2509.02852). The long, diverse history of such intervals is closely related…
PHYSTAT Informal Review: Marginalizing versus Profiling of Nuisance Parameters
Robert D. Cousins, Larry Wasserman
This is a writeup, with some elaboration, of the talks by the two authors (a physicist and a statistician) at the first PHYSTAT Informal review on January 24, 2024. We discuss Baye…
What is the likelihood function, and how is it used in particle physics?
Robert D. Cousins
Likelihood functions are ubiquitous in data analyses at the LHC and elsewhere in particle physics. Partly because "probability" and "likelihood" are virtual synonyms in everyday En…
Lectures on Statistics in Theory: Prelude to Statistics in Practice
Robert D. Cousins
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…
Should unfolded histograms be used to test hypotheses?
Robert D. Cousins, Samuel J. May, Yipeng Sun
In many analyses in high energy physics, attempts are made to remove the effects of detector smearing in data by techniques referred to as "unfolding" histograms, thus obtaining es…
Negatively Biased Relevant Subsets Induced by the Most-Powerful One-Sided Upper Confidence Limits for a Bounded Physical Parameter
Robert D. Cousins
Suppose an observable x is the measured value (negative or non-negative) of a true mean mu (physically non-negative) in an experiment with a Gaussian resolution function with known…
Frequentist Evaluation of Intervals Estimated for a Binomial Parameter and for the Ratio of Poisson Means
Robert D. Cousins, Kathryn E. Hymes, Jordan Tucker
Confidence intervals for a binomial parameter or for the ratio of Poisson means are commonly desired in high energy physics (HEP) applications such as measuring a detection efficie…
Kalman Filter Track Fits and Track Breakpoint Analysis
Pierre Astier, Alessandro Cardini, Robert D. Cousins +3
We give an overview of track fitting using the Kalman filter method in the NOMAD detector at CERN, and emphasize how the wealth of by-product information can be used to analyze tra…
A Unified Approach to the Classical Statistical Analysis of Small Signals
Gary J. Feldman, Robert D. Cousins
We give a classical confidence belt construction which unifies the treatment of upper confidence limits for null results and two-sided confidence intervals for non-null results. Th…