Combined Neyman–Pearson chi-square: An improved approximation to the Poisson-likelihood chi-square

Ji, Xiangpan; Gu, Wenqiang; Qian, Xin; Wei, Hanyu; Zhang, Chao

doi:10.1016/j.nima.2020.163677

Combined Neyman–Pearson chi-square: An improved approximation to the Poisson-likelihood chi-square

Journal Article · Sat Feb 22 00:00:00 EST 2020 · Nuclear Instruments and Methods in Physics Research. Section A, Accelerators, Spectrometers, Detectors and Associated Equipment

DOI:https://doi.org/10.1016/j.nima.2020.163677· OSTI ID:1603273

Ji, Xiangpan ^[1]; Gu, Wenqiang ^[1]; Qian, Xin ^[1]; Wei, Hanyu ^[1]; Zhang, Chao ^[1]

Brookhaven National Lab. (BNL), Upton, NY (United States)

We describe an approximation to the widely-used Poisson-likelihood chi-square using a linear combination of Neyman’s and Pearson’s chi-squares, namely “combined Neyman–Pearson chi-square” ($$X^2_{CNP}$$). Through analytical derivations and toy model simulations, we show that leads to a significantly smaller bias on the best-fit model parameters compared to those using either Neyman’s or Pearson’s chi-square. When the computational cost of using the Poisson-likelihood chi-square is high, $$X^2_{CNP}$$ provides a good alternative given its natural connection to the covariance matrix formalism.

View Accepted Manuscript (DOE)

Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

Grant/Contract Number:: SC0012704

OSTI ID:: 1603273

Alternate ID(s):: OSTI ID: 1601521

Report Number(s):: BNL--213688-2020-JAAM

Journal Information:: Nuclear Instruments and Methods in Physics Research. Section A, Accelerators, Spectrometers, Detectors and Associated Equipment, Journal Name: Nuclear Instruments and Methods in Physics Research. Section A, Accelerators, Spectrometers, Detectors and Associated Equipment Journal Issue: C Vol. 961; ISSN 0168-9002

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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