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We propose a novel estimator of the polarization amplitude from a single measurement of its normally distributed $(Q,U)$ Stokes components. Based on the properties of the Rice distribution and dubbed MAS (Modified ASymptotic), it meets several desirable criteria:(i) its values lie in the whole positive region; (ii) its distribution is continuous; (iii) it transforms smoothly with the signal-to-noise ratio (SNR) from a Rayleigh-like shape to a Gaussian one; (iv) it is unbiased and reaches its components variance as soon as the SNR exceeds 2; (v) it is analytic and can therefore be used on large data-sets. We also revisit the construction of its associated confidence intervals and show how the Feldman-Cousins prescription efficiently solves the issue of classical intervals lying entirely in the unphysical negative domain. Such intervals can be used to identify statistically significant polarized regions and conversely build masks for polarization data. We then consider the case of a general $[Q,U]$ covariance matrix and perform a generalization of the estimator that preserves its asymptotic properties. We show that its bias does not depend on the true polarization angle, and provide an analytic estimate of its variance. The estimator value, together with its variance, provide a powerful point-estimate of the true polarization amplitude that follows an unbiased Gaussian distribution for a SNR as low as 2. These results can be applied to the much more general case of transforming any normally distributed random variable from Cartesian to polar coordinates.
In this paper we present a parameter estimation analysis of the polarization and temperature power spectra from the second and third season of observations with the QUaD experiment. QUaD has for the first time detected multiple acoustic peaks in the
We propose an operational degree of polarization in terms of the variance of the projected Stokes vector minimized over all the directions of the Poincare sphere. We examine the properties of this degree and show that some problems associated with th
Network data sets are often constructed by some kind of thresholding procedure. The resulting networks frequently possess properties such as heavy-tailed degree distributions, clustering, large connected components and short average shortest path len
We introduce a new estimator of the peculiar velocity of a galaxy or group of galaxies from redshift and distance estimates. This estimator results in peculiar velocity estimates which are statistically unbiased and that have errors that are Gaussian
We present ECLIPSE (Efficient Cmb poLarization and Intensity Power Spectra Estimator), an optimized implementation of the Quadratic Maximum Likelihood (QML) method for the estimation of the power spectra of the Cosmic Microwave Background (CMB). This