Nuisance parameter problem in quantum estimation theory: tradeoff relation and qubit examples

AbstractThe paper aims to develop an effective preconditioner and conduct the convergence analysis of the corresponding preconditioned GMRES for the solution of discrete problems originating from multi-group radiation diffusion equations. We firstly investigate the performances of the most widely used preconditioners (ILU(k) and AMG) and their combinations (Bco and Bco), and provide drawbacks on their feasibilities. Secondly, we reveal the underlying complementarity of ILU(k) and AMG by analyzing the features suitable for AMG using more detailed measurements on multiscale nature of matrices and the effect of ILU(k) on multiscale nature. Moreover, we present an adaptive combined preconditioner Bcoα involving an improved ILU(0) along with its convergence constraints. Numerical results demonstrate that Bcoα-GMRES holds the best robustness and efficiency. At last, we analyze the convergence of GMRES with combined preconditioning which not only provides a persuasive support for our proposed algorithms, but also updates the existing estimation theory on condition numbers of combined preconditioned systems.

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Statistical parameter estimation theory: principles and simulation studies

10.1016/bs.aiep.2021.01.002 ◽

2021 ◽

Author(s):

Annick De Backer ◽

Jarmo Fatermans ◽

Arnold J. den Dekker ◽

Sandra Van Aert

Keyword(s):

Parameter Estimation ◽

Statistical Parameter ◽

Estimation Theory ◽

Simulation Studies ◽

Statistical Parameter Estimation

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The degeneracy between primordial non-Gaussianity and foregrounds in 21 cm intensity mapping experiments

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa2986 ◽

2020 ◽

Vol 499 (3) ◽

pp. 4054-4067

Author(s):

Steven Cunnington ◽

Stefano Camera ◽

Alkistis Pourtsidou

Keyword(s):

Nuisance Parameter ◽

Neutral Hydrogen ◽

Real Data ◽

Line Of Sight ◽

Markov Chain Analysis ◽

Significant Progress ◽

Intensity Mapping ◽

Chain Analysis ◽

Parallel Text ◽

Foreground Removal

ABSTRACT Potential evidence for primordial non-Gaussianity (PNG) is expected to lie in the largest scales mapped by cosmological surveys. Forthcoming 21 cm intensity mapping experiments will aim to probe these scales by surveying neutral hydrogen (H i) within galaxies. However, foreground signals dominate the 21 cm emission, meaning foreground cleaning is required to recover the cosmological signal. The effect this has is to damp the H i power spectrum on the largest scales, especially along the line of sight. Whilst there is agreement that this contamination is potentially problematic for probing PNG, it is yet to be fully explored and quantified. In this work, we carry out the first forecasts on fNL that incorporate simulated foreground maps that are removed using techniques employed in real data. Using an Monte Carlo Markov Chain analysis on an SKA1-MID-like survey, we demonstrate that foreground cleaned data recovers biased values [$f_{\rm NL}= -102.1_{-7.96}^{+8.39}$ (68 per cent CL)] on our fNL = 0 fiducial input. Introducing a model with fixed parameters for the foreground contamination allows us to recover unbiased results ($f_{\rm NL}= -2.94_{-11.9}^{+11.4}$). However, it is not clear that we will have sufficient understanding of foreground contamination to allow for such rigid models. Treating the main parameter $k_\parallel ^\text{FG}$ in our foreground model as a nuisance parameter and marginalizing over it, still recovers unbiased results but at the expense of larger errors ($f_{\rm NL}= 0.75^{+40.2}_{-44.5}$), which can only be reduced by imposing the Planck 2018 prior. Our results show that significant progress on understanding and controlling foreground removal effects is necessary for studying PNG with H i intensity mapping.

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Efficient Localization Algorithm for Near-Field Noncircular Sources via Dual-Polarization Sensor Array

Mathematical Problems in Engineering ◽

10.1155/2019/5759427 ◽

2019 ◽

Vol 2019 ◽

pp. 1-8

Author(s):

Jiaqi Song ◽

Haihong Tao

Keyword(s):

Source Localization ◽

Near Field ◽

Nuisance Parameter ◽

Estimation Accuracy ◽

Localization Algorithm ◽

Dual Polarization ◽

Rank Reduction ◽

Localization Accuracy ◽

Noncircular Signals ◽

Polarization Sensor

Noncircular signals are widely used in the area of radar, sonar, and wireless communication array systems, which can offer more accurate estimates and detect more sources. In this paper, the noncircular signals are employed to improve source localization accuracy and identifiability. Firstly, an extended real-valued covariance matrix is constructed to transform complex-valued computation into real-valued computation. Based on the property of noncircular signals and symmetric uniform linear array (SULA) which consist of dual-polarization sensors, the array steering vectors can be separated into the source position parameters and the nuisance parameter. Therefore, the rank reduction (RARE) estimators are adopted to estimate the source localization parameters in sequence. By utilizing polarization information of sources and real-valued computation, the maximum number of resolvable sources, estimation accuracy, and resolution can be improved. Numerical simulations demonstrate that the proposed method outperforms the existing methods in both resolution and estimation accuracy.

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On the Spectral Parameter Problem

Acta Applicandae Mathematicae ◽

10.1007/s10440-009-9450-4 ◽

2009 ◽

Vol 109 (1) ◽

pp. 239-255 ◽

Cited By ~ 17

Author(s):

Michal Marvan

Keyword(s):

Spectral Parameter ◽

Parameter Problem

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The Concentration Ellipsoid of a Random Vector Revisited

Econometric Theory ◽

10.1017/s0266466600004539 ◽

1991 ◽

Vol 7 (3) ◽

pp. 397-403 ◽

Cited By ~ 2

Author(s):

Kenneth Nordström

Keyword(s):

Quadratic Form ◽

Random Vector ◽

Crucial Role ◽

Type Inequality ◽

Estimation Theory ◽

Linear Estimation ◽

Nonnegative Definite

Alternative definitions of the concentration ellipsoid of a random vector are surveyed, and an extension of the concentration ellipsoid of Darmois is suggested as being the most convenient and natural definition. The advantage of the proposed definition in providing substantially simplified proofs of results in (linear) estimation theory is discussed, and is illustrated by new and short proofs of two key results. A not-so-well-known, but elementary, extremal representation of a nonnegative definite quadratic form, together with the corresponding Cauchy-Schwarẓ-type inequality, is seen to play a crucial role in these proofs.

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