Probability density functions, f2D(p,ψ | I0,p0,ψ0,Σ), with finite S/N on intensity, I0/σI = 1, 2, and 5 (columns from left to right), computed for a given set of polarization parameters, ψ0 = 0° and p0 = 0.1 (dashed lines), and a S/N on the polarized intensity set to p0/σp,G = 1. Correlation coefficients ρQ and ρU are set to zero. Various configurations of the covariance matrix are shown (rows). White crosses indicate the mean likelihood estimates of the PDF (). The contour levels are provided at 0.1, 1, 5, 10, 20, 50, 70, and 90% of the maximum of the distribution. The polarization fraction is here defined over both the negative and positive ranges, due to the noise of the intensity.
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