On characterizing the complex Wishart distribution

In this research paper, we generalized the results of Ignacy in the multivariate case in order to characterize the complex Wishart distribution.

A Novel Anti-Jamming Technique for INS/GNSS Integration Based on Black Box Variational Inference

In this paper, a novel anti-jamming technique based on black box variational inference for INS/GNSS integration with time-varying measurement noise covariance matrices is presented. We proved that the time-varying measurement noise is more similar to the Gaussian distribution with time-varying mean value than to the Inv-Gamma or Inv-Wishart distribution found by Kullback–Leibler divergence. Therefore, we assumed the prior distribution of measurement noise covariance matrices as Gaussian, and calculated the Gaussian parameters by the black box variational inference method. Finally, we obtained the measurement noise covariance matrices by using the Gaussian parameters. The experimental results illustrate that the proposed algorithm performs better in resisting time-varying measurement noise than the existing Variational Bayesian adaptive filter.

Detecting Changes in Fully Polarimetric SAR Imagery With Statistical Information Theory

© 1980-2012 IEEE. Images obtained from coherent illumination processes are contaminated with speckle. A prominent example of such imagery systems is the polarimetric synthetic aperture radar (PolSAR). For such a remote sensing tool, the speckle interference pattern appears in the form of a positive-definite Hermitian matrix, which requires specialized models and makes change detection a hard task. The scaled complex Wishart distribution is a widely used model for PolSAR images. Such a distribution is defined by two parameters: the number of looks and the complex covariance matrix. The last parameter contains all the necessary information to characterize the backscattered data, and thus, identifying changes in a sequence of images can be formulated as a problem of verifying whether the complex covariance matrices differ at two or more takes. This paper proposes a comparison between a classical change detection method based on the likelihood ratio and three statistical methods that depend on information-theoretic measures: the Kullback-Leibler (KL) distance and two entropies. The performance of these four tests was quantified in terms of their sample test powers and sizes using simulated data. The tests are then applied to actual PolSAR data. The results provide evidence that tests based on entropies may outperform those based on the KL distance and likelihood ratio statistics.

Detecting Changes in Fully Polarimetric SAR Imagery With Statistical Information Theory

© 1980-2012 IEEE. Images obtained from coherent illumination processes are contaminated with speckle. A prominent example of such imagery systems is the polarimetric synthetic aperture radar (PolSAR). For such a remote sensing tool, the speckle interference pattern appears in the form of a positive-definite Hermitian matrix, which requires specialized models and makes change detection a hard task. The scaled complex Wishart distribution is a widely used model for PolSAR images. Such a distribution is defined by two parameters: the number of looks and the complex covariance matrix. The last parameter contains all the necessary information to characterize the backscattered data, and thus, identifying changes in a sequence of images can be formulated as a problem of verifying whether the complex covariance matrices differ at two or more takes. This paper proposes a comparison between a classical change detection method based on the likelihood ratio and three statistical methods that depend on information-theoretic measures: the Kullback-Leibler (KL) distance and two entropies. The performance of these four tests was quantified in terms of their sample test powers and sizes using simulated data. The tests are then applied to actual PolSAR data. The results provide evidence that tests based on entropies may outperform those based on the KL distance and likelihood ratio statistics.

Sufficiency of a Gaussian power spectrum likelihood for accurate cosmology from upcoming weak lensing surveys

We investigate whether a Gaussian likelihood is sufficient to obtain accurate parameter constraints from a Euclid-like combined tomographic power spectrum analysis of weak lensing, galaxy clustering and their cross-correlation. Testing its performance on the full sky against the Wishart distribution, which is the exact likelihood under the assumption of Gaussian fields, we find that the Gaussian likelihood returns accurate parameter constraints. This accuracy is robust to the choices made in the likelihood analysis, including the choice of fiducial cosmology, the range of scales included, and the random noise level. We extend our results to the cut sky by evaluating the additional non-Gaussianity of the joint cut-sky likelihood in both its marginal distributions and dependence structure. We find that the cut-sky likelihood is more non-Gaussian than the full-sky likelihood, but at a level insufficient to introduce significant inaccuracy into parameter constraints obtained using the Gaussian likelihood. Our results should not be affected by the assumption of Gaussian fields, as this approximation only becomes inaccurate on small scales, which in turn corresponds to the limit in which any non-Gaussianity of the likelihood becomes negligible. We nevertheless compare against N-body weak lensing simulations and find no evidence of significant additional non-Gaussianity in the likelihood. Our results indicate that a Gaussian likelihood will be sufficient for robust parameter constraints with power spectra from Stage IV weak lensing surveys.

Confirmatory Factor Analysis of MUIS-C Scale Among Baby Boomers With Hepatitis C

Background and PurposeThe purpose of this study was to evaluate Mishel Uncertainty in Illness Scale—Community (MUIS-C), used to gauge level of uncertainty among baby boomers with hepatitis C virus (HCV) infection, as a reliable two-factor instrument.MethodsA CFA was conducted to test MUIS-C. There were minor deviations from normality. Subsequently, 130 participants were used to examine the factor structure and the model fit. A robust maximum likelihood (ML) estimation using the Wishart distribution was implemented in R version 3.3.1.ResultsA very good model fit was obtained (𝜒2(101) = 118.32, p = .115, TLI = 0.977, CFI = 0.983, RMSEA = 0.036, 90%CI(0.000, 0.061), and SRMR = 0.057). All indicators showed significant positive factor loadings, with standardized coefficients ranging from 0.511 to 0.868.ConclusionsThe MUIS-C was a reliable two-factor instrument and suitable for use as such in baby boomer population with HCV.