A note on estimating errors from the likelihood function

Roger Barlow

doi:10.1016/j.nima.2005.05.047

A note on estimating errors from the likelihood function

Roger Barlow

Research output: Contribution to journal › Article › peer-review

Abstract

The points at which the log likelihood falls by 12 from its maximum value are often used to give the 'errors' on a result, i.e. the 68% central confidence interval. The validity of this is examined for two simple cases: a lifetime measurement and a Poisson measurement. Results are compared with the exact Neyman construction and with the simple Bartlett approximation. It is shown that the accuracy of the log likelihood method is poor, and the Bartlett construction explains why it is flawed. © 2005 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	392-396
Number of pages	4
Journal	Nuclear Instruments & Methods in Physics Research. Section A: Accelerators, Spectrometers, Detectors, and Associated Equipment
Volume	550
Issue number	1-2
DOIs	https://doi.org/10.1016/j.nima.2005.05.047
Publication status	Published - 11 Sept 2005

Keywords

Confidence interval
Errors
Maximum likelihood

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10.1016/j.nima.2005.05.047

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abstract = "The points at which the log likelihood falls by 12 from its maximum value are often used to give the 'errors' on a result, i.e. the 68\% central confidence interval. The validity of this is examined for two simple cases: a lifetime measurement and a Poisson measurement. Results are compared with the exact Neyman construction and with the simple Bartlett approximation. It is shown that the accuracy of the log likelihood method is poor, and the Bartlett construction explains why it is flawed. {\textcopyright} 2005 Elsevier B.V. All rights reserved.",

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AB - The points at which the log likelihood falls by 12 from its maximum value are often used to give the 'errors' on a result, i.e. the 68% central confidence interval. The validity of this is examined for two simple cases: a lifetime measurement and a Poisson measurement. Results are compared with the exact Neyman construction and with the simple Bartlett approximation. It is shown that the accuracy of the log likelihood method is poor, and the Bartlett construction explains why it is flawed. © 2005 Elsevier B.V. All rights reserved.

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KW - Errors

KW - Maximum likelihood

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JO - Nuclear Instruments & Methods in Physics Research. Section A: Accelerators, Spectrometers, Detectors, and Associated Equipment

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IS - 1-2

ER -

A note on estimating errors from the likelihood function

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Keywords

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