87,176 research outputs found
Performance test of QU-fitting in cosmic magnetism study
QU-fitting is a standard model-fitting method to reconstruct distribution of
magnetic fields and polarized intensity along a line of sight (LOS) from an
observed polarization spectrum. In this paper, we examine the performance of
QU-fitting by simulating observations of two polarized sources located along
the same LOS, varying the widths of the sources and the gap between them in
Faraday depth space, systematically. Markov Chain Monte Carlo (MCMC) approach
is used to obtain the best-fit parameters for a fitting model, and Akaike and
Bayesian Information Criteria (AIC and BIC, respectively) are adopted to select
the best model from four fitting models. We find that the combination of MCMC
and AIC/BIC works fairly well in model selection and estimation of model
parameters in the cases where two sources have relatively small widths and a
larger gap in Faraday depth space. On the other hand, when two sources have
large width in Faraday depth space, MCMC chain tends to be trapped in a local
maximum so that AIC/BIC cannot select a correct model. We discuss the causes
and the tendency of the failure of QU-fitting and suggest a way to improve it.Comment: 8 pages, 9 figures, submitted to MNRA
Accounting for Calibration Uncertainties in X-ray Analysis: Effective Areas in Spectral Fitting
While considerable advance has been made to account for statistical
uncertainties in astronomical analyses, systematic instrumental uncertainties
have been generally ignored. This can be crucial to a proper interpretation of
analysis results because instrumental calibration uncertainty is a form of
systematic uncertainty. Ignoring it can underestimate error bars and introduce
bias into the fitted values of model parameters. Accounting for such
uncertainties currently requires extensive case-specific simulations if using
existing analysis packages. Here we present general statistical methods that
incorporate calibration uncertainties into spectral analysis of high-energy
data. We first present a method based on multiple imputation that can be
applied with any fitting method, but is necessarily approximate. We then
describe a more exact Bayesian approach that works in conjunction with a Markov
chain Monte Carlo based fitting. We explore methods for improving computational
efficiency, and in particular detail a method of summarizing calibration
uncertainties with a principal component analysis of samples of plausible
calibration files. This method is implemented using recently codified Chandra
effective area uncertainties for low-resolution spectral analysis and is
verified using both simulated and actual Chandra data. Our procedure for
incorporating effective area uncertainty is easily generalized to other types
of calibration uncertainties.Comment: 61 pages double spaced, 8 figures, accepted for publication in Ap
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