Placing Confidence Limits on Polarization Measurements
Author(s) -
John E. Vaillancourt
Publication year - 2006
Publication title -
publications of the astronomical society of the pacific
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.294
H-Index - 172
eISSN - 1538-3873
pISSN - 0004-6280
DOI - 10.1086/507472
Subject(s) - polarization (electrochemistry) , confidence interval , likelihood function , physics , bayesian probability , statistics , computational physics , optics , environmental science , mathematics , maximum likelihood , chemistry
The determination of the true source polarization given a set of measurementsis complicated by the requirement that the polarization always be positive.This positive bias also hinders construction of upper limits, uncertainties,and confidence regions, especially at low signal-to-noise levels. We generatethe likelihood function for linear polarization measurements and use it tocreate confidence regions and upper limits. This is accomplished by integratingthe likelihood function over the true polarization (parameter space), ratherthan the measured polarization (data space). These regions are valid for bothlow and high signal-to-noise measurements.Comment: 8 pages, 3 figures, 1 table, submitted to PAS
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