Neyman & Feldman-Cousins intervals for a simple problem with an unphysical region, and an analytic solution

2006/04/28 by B. D. Yabsley, B. Yabsley, Yabsley, B. D.
Computer Science · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Data Analysis #FOS: Physical sciences #High Energy Physics - Experiment (hep-ex) #Statistics and Probability (physics.data-an) #hep-ex #physics.data-an

paper · pdf · doi:10.48550/arxiv.hep-ex/0604055

10 pages, 3 figures

arxiv created 2006/04/28 · openalex publication_date 2006/04/28 · arxiv updated 2009/12/01 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

The new Belle phi₃/gamma measurement arXiv:hep-ex/0604054, based on Dalitz analysis of D -> Kshort pi+ pi- in B+- -> D(*) K(*)+- decays, uses likelihood ratio ordering to set confidence intervals in phi₃ and the r,delta parameters. This is different to the choice made by BaBar in PRL 95, 121802 (2005) and arXiv:hep-ex/0507101, and requires additional computation. This Note explains Belle's choice using a related but simpler example: the averaging of two numbers. We find that intervals calculated with likelihood ratio ordering reproduce the analytic solution to this problem, whereas intervals calculated by ordering according to the p.d.f. (so-called Neyman intervals) do not, and show a pathology which is important in our case. This document is adapted from a Belle Internal Note.

Citations

• Measurement of gamma in B-+ -> D(*) K-+ and B-+ -> D K*-+ decays with a Dalitz analysis of D -> Ks pi- pi+

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