Related papers: Placing Confidence Limits on Polarization Measurem…
A fully analytic statistical formalism does not yet exist to describe radio-wavelength measurements of linearly polarized intensity that are produced using rotation measure synthesis. In this work we extend the analytic formalism for…
High precision polarization measurements open new opportunities for the study of the magnetic field structure as traced by polarimetric measurements of the interstellar dust emission. Polarization parameters suffer from bias in the presence…
Most existing works of polar codes focus on the analysis of block error probability. However, in many scenarios, bit error probability is also important for evaluating the performance of channel codes. In this paper, we establish a new…
We develop two algorithms, based on maximum likelihood (ML) inference, for estimating the parameters of polarized radio sources which emit at a single rotation measure (RM), e.g., pulsars. These algorithms incorporate the flux density…
This contribution to the debate on confidence limits focuses mostly on the case of measurements with `open likelihood', in the sense that it is defined in the text. I will show that, though a prior-free assessment of {\it confidence} is, in…
A detailed and formal account of polarization measurements using Bayesian analysis is given based on the assumption of gaussian error for the Stokes parameters. This analysis is crucial for the measurement of the polarization degree and…
Radio sources are often polarized. Accurate measurement of simply the flux density of a radio source requires a basic understanding of polarization and its measurement techniques. We provide an introductory, heuristic discussion of these…
We benchmark the reliability of the Rotation Measure (RM) synthesis algorithm using the 1005 Centaurus A field sources of Feain et al. (2009). The RM synthesis solutions are compared with estimates of the polarization parameters using…
Confidence limits are common place in physics analysis. Great care must be taken in their calculation and use, especially in cases of limited statistics when often one-sided limits are quoted. In order to estimate the stability of the…
Microwave background temperature and polarization observations are a powerful way to constrain cosmological parameters if the likelihood function can be calculated accurately. The temperature and polarization fields are correlated, partial…
Quantifying the amount of polarization is crucial for understanding and studying political polarization in political and social systems. Several methods are used commonly to measure polarization in social networks by purely inspecting their…
With the forthcoming release of high precision polarization measurements, such as from the Planck satellite, the metrology of polarization needs to improve. In particular, it is crucial to take into account full knowledge of the noise…
A number of polarization estimators have been developed for a variety of astrophysical applications to compensate measurements of linear polarization for a bias contributed by the instrumental noise. Most derivations of the estimators…
We discuss a new method for setting limits on small signals in the presence of background noise. The method is based on a combination of a two dimensional confidence region and the large sample approximation to the likelihood ratio test…
In many polarimetry applications, including observations in the X-ray band, the measurement of a polarization signal can be reduced to the detection and quantification of a deviation from uniformity of a distribution of measured angles. We…
Measuring the alignment of polarized radio sources requires comparing vectors at different locations on the sky, i.e. on a sphere. A test of alignment is derived herein. While both large scale and coordinate independent, the test avoids the…
We show on theoretical grounds that, even in the presence of noise, probabilistic measurement strategies (which have a certain probability of failure or abstention) can provide, upon a heralded successful outcome, estimates with a precision…
Astrophysical polarization measurements provide some of the strongest constraints on the photon sector of the non-minimal Standard-Model Extension. This paper reviews some recent results obtained by combining optical linear and circular…
AIMS. The maximum-likelihood method is the standard approach to obtain model fits to observational data and the corresponding confidence regions. We investigate possible sources of bias in the log-likelihood function and its subsequent…
Polarization arises when the underlying network connecting the members of a community or society becomes characterized by highly connected groups with weak inter-group connectivity. The increasing polarization, the strengthening of echo…