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Register a new userTowards reliable uncertainties in IR interferometry: The bootstrap for correlated statistical & systematic errors
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We propose a method to overcome the usual limitation of current data processing techniques in optical and infrared long-baseline interferometry: most reduction pipelines assume uncorrelated statistical errors and ignore systematics. We use the bootstrap method to sample the multivariate probability density function of the interferometric observables. It allows us to determine the correlations between statistical error terms and their deviation from a Gaussian distribution. In addition, we introduce systematics as an additional, highly correlated error term whose magnitude is chosen to fit the data dispersion. We have applied the method to obtain accurate measurements of stellar diameters for under-resolved stars, i.e. smaller than the angular resolution of the interferometer. We show that taking correlations and systematics has a significant impact on both the diameter estimate and its uncertainty. The robustness of our diameter determination comes at a price: we obtain 4 times larger uncertainties, of a few percent for most stars in our sample.
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Very Long Baseline Interferometric (VLBI) observations of quasar jets enable one to measure many theoretically expected effects. Estimating the significance of observational findings is complicated by the correlated noise in the image plane. A reliable and well justified approach to estimate the uncertainties of VLBI results is needed as well as significance testing criteria. We propose to use bootstrap for both tasks. Using simulations we find that bootstrap-based errors for the full intensity, rotation measure, and spectral index maps have coverage closer to the nominal values than conventionally obtained errors. The proposed method naturally takes into account heterogeneous interferometric arrays (such as Space VLBI) and can be easily extended to account for instrumental calibration factors.
The influence of systematic errors on the calculation of the statistical significance of a $gamma$-ray signal with the frequently invoked Li and Ma method is investigated. A simple criterion is derived to decide whether the Li and Ma method can be applied in the presence of systematic errors. An alternative method is discussed for cases where systematic errors are too large for the application of the original Li and Ma method. This alternative method reduces to the Li and Ma method when systematic errors are negligible. Finally, it is shown that the consideration of systematic errors will be important in many analyses of data from the planned Cherenkov Telescope Array.
Context. Monte Carlo methods can be used to evaluate the uncertainty of a reaction rate that arises from many uncertain nuclear inputs. However, until now no attempt has been made to find the effect of correlated energy uncertainties in input resonance parameters. Aims. To investigate the impact of correlated energy uncertainties on reaction rates. Methods. Using a combination of numerical and Monte Carlo variation of resonance energies, the effect of correlations are investigated. Five reactions are considered: two fictional, illustrative cases and three reactions whose rates are of current interest. Results. The effect of correlations in resonance energies depends on the specific reaction cross section and temperatures considered. When several resonances contribute equally to a reaction rate, and are located either side of the Gamow peak, correlations between their energies dilute their effect on reaction rate uncertainties. If they are both located above or below the maximum of the Gamow peak, however, correlations between their resonance energies can increase the reaction rate uncertainties. This effect can be hard to predict for complex reactions with wide and narrow resonances contributing to the reaction rate.
In this proceeding, we present studies of instrumental systematic effects for the Simons Obsevatory (SO) that are associated with the detector system and its interaction with the full SO experimental systems. SO will measure the Cosmic Microwave Background (CMB) temperature and polarization anisotropies over a wide range of angular scales in six bands with bandcenters spanning from 27 GHz to 270 GHz. We explore effects including intensity-to-polarization leakage due to coupling optics, bolometer nonlinearity, uncalibrated gain variations of bolometers, and readout crosstalk. We model the level of signal contamination, discuss proposed mitigation schemes, and present instrument requirements to inform the design of SO and future CMB projects.
The Simons Observatory (SO) will observe the temperature and polarization anisotropies of the cosmic microwave background (CMB) over a wide range of frequencies (27 to 270 GHz) and angular scales by using both small (0.5 m) and large (6 m) aperture telescopes. The SO small aperture telescopes will target degree angular scales where the primordial B-mode polarization signal is expected to peak. The incoming polarization signal of the small aperture telescopes will be modulated by a cryogenic, continuously-rotating half-wave plate (CRHWP) to mitigate systematic effects arising from slowly varying noise and detector pair-differencing. In this paper, we present an assessment of some systematic effects arising from using a CRHWP in the SO small aperture systems. We focus on systematic effects associated with structural properties of the HWP and effects arising when operating a HWP, including the amplitude of the HWP synchronous signal (HWPSS), and I -> P (intensity to polarization) leakage that arises from detector non-linearity in the presence of a large HWPSS. We demonstrate our ability to simulate the impact of the aforementioned systematic effects in the time domain. This important step will inform mitigation strategies and design decisions to ensure that SO will meet its science goals.
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