Placing Confidence Limits on Polarization Measurements

By J. Vaillancourt. 2006

155 citations recorded by the source corpus.

The determination of the true source polarization given a set of measurements is 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 ratios (S/Ns). We take a Bayesian approach to creating confidence regions and upper limits by integrating over the likelihood function for polarization measurements. These regions are valid for both low‐ and high‐S/N measurements.

Subfields: Astronomy and Astrophysics, Biomedical Engineering, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/50e14c73eba57c609bc9a5ed8601313f1f330d60

How researchers see this paper

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In Astronomy and Astrophysics

1. T. Pillai
2. G. Bower
3. R. Crutcher
4. L. Looney
5. J. Vaillancourt
6. R. Plambeck
7. L. Fissel
8. Christoph Federrath

Citations in the corpus

• TADPOL: A 1.3 mm SURVEY OF DUST POLARIZATION IN STAR-FORMING CORES AND REGIONS (2013, methodology): “5σP , we calculated Pc by finding the maximum of the probability distribution function (i.e., the most probable value) of the true polarization Pc given the observed polarization P (see Vaillancourt 2006).”
• THE LEGACY OF SCUPOL: 850 μm IMAGING POLARIMETRY FROM 1997 TO 2005 (2009, background): “A bias exists that tends to increase the polarization percentage value, even when Q and U are consistent with a value of zero because polarization percentage is forced to be positive (Vaillancourt 2006).”
• Polarization of the Crab Pulsar and Nebula as Observed by the INTEGRAL/IBIS Telescope (2008, unknown): “…a and ψ from Npt independent data points in N(ψ) over a π period, based on Gaussian distributions for the orthogonal Stokes components (Weisskopf 2006, Vaillancourt 2006, Vinokur 1965): dP (a, ψ) = Npt S 2 π σ2S exp[− Npt S 2 2 σ2S [a2 + a20 − 2aa0cos(2ψ − 2ψ0)]] a da dψ (2) σS notes the error…”