55,032 research outputs found
Covariance Intersection in Nonlinear Estimation Based on Pseudo Gaussian Densities
Many modern fusion architectures are designed to process and fuse data in networked systems. Alongside the advantages, such as scalability and robustness, distributed fusion techniques particularly have to tackle the problem of dependencies between locally processed data. In linear estimation problems, uncertain quantities with unknown cross-correlations can be fused by means of the covariance intersection algorithm, which avoids overconfident fusion results. However, for nonlinear system dynamics and sensor models perturbed by arbitrary noise, it is not only a problem to characterize and parameterize dependencies between estimates, but also to find a proper notion of consistency. This paper addresses these issues by transforming the state estimates to a different state space, where the corresponding densities are Gaussian and only linear dependencies between estimates, i.e., correlations, can arise. These pseudo Gaussian densities then allow the notion of covariance consistency to be used in distributed nonlinear state estimation
Enhancing hyperspectral image unmixing with spatial correlations
This paper describes a new algorithm for hyperspectral image unmixing. Most
of the unmixing algorithms proposed in the literature do not take into account
the possible spatial correlations between the pixels. In this work, a Bayesian
model is introduced to exploit these correlations. The image to be unmixed is
assumed to be partitioned into regions (or classes) where the statistical
properties of the abundance coefficients are homogeneous. A Markov random field
is then proposed to model the spatial dependency of the pixels within any
class. Conditionally upon a given class, each pixel is modeled by using the
classical linear mixing model with additive white Gaussian noise. This strategy
is investigated the well known linear mixing model. For this model, the
posterior distributions of the unknown parameters and hyperparameters allow
ones to infer the parameters of interest. These parameters include the
abundances for each pixel, the means and variances of the abundances for each
class, as well as a classification map indicating the classes of all pixels in
the image. To overcome the complexity of the posterior distribution of
interest, we consider Markov chain Monte Carlo methods that generate samples
distributed according to the posterior of interest. The generated samples are
then used for parameter and hyperparameter estimation. The accuracy of the
proposed algorithms is illustrated on synthetic and real data.Comment: Manuscript accepted for publication in IEEE Trans. Geoscience and
Remote Sensin
Modelling Volatilities and Conditional Correlations in Futures Markets with a Multivariate t Distribution
This paper considers a multivariate t version of the Gaussian dynamic conditional correlation (DCC) model proposed by Engle (2002), and suggests the use of devolatized returns computed as returns standardized by realized volatilities rather than by GARCH type volatility estimates. The
t-DCC estimation procedure is applied to a portfolio of daily returns on currency futures, government bonds and equity index futures. The results strongly reject the normal-DCC model in favour of a t-DCC specification. The t-DCC model also passes a number of VaR diagnostic tests over an evaluation sample. The estimation results suggest a general trend towards a lower level of return volatility, accompanied by a rising trend in conditional cross correlations in most markets; possibly reflecting the advent of euro in 1999 and increased interdependence of financial markets
Simulating the Large-Scale Structure of HI Intensity Maps
Intensity mapping of neutral hydrogen (HI) is a promising observational probe
of cosmology and large-scale structure. We present wide field simulations of HI
intensity maps based on N-body simulations of a box with
particles (particle mass ).
Using a conditional mass function to populate the simulated dark matter density
field with halos below the mass resolution of the simulation (), we assign HI to
those halos according to a phenomenological halo to HI mass relation. The
simulations span a redshift range of 0.35 < z < 0.9 in redshift bins of width
and cover a quarter of the sky at an angular resolution
of about 7'. We use the simulated intensity maps to study the impact of
non-linear effects and redshift space distortions on the angular clustering of
HI. Focusing on the autocorrelations of the maps, we apply and compare several
estimators for the angular power spectrum and its covariance. We verify that
these estimators agree with analytic predictions on large scales and study the
validity of approximations based on Gaussian random fields, particularly in the
context of the covariance. We discuss how our results and the simulated maps
can be useful for planning and interpreting future HI intensity mapping
surveys.Comment: 35 pages, 19 Figures. Accepted for publication in JCA
Credit Risk Meets Random Matrices: Coping with Non-Stationary Asset Correlations
We review recent progress in modeling credit risk for correlated assets. We
start from the Merton model which default events and losses are derived from
the asset values at maturity. To estimate the time development of the asset
values, the stock prices are used whose correlations have a strong impact on
the loss distribution, particularly on its tails. These correlations are
non-stationary which also influences the tails. We account for the asset
fluctuations by averaging over an ensemble of random matrices that models the
truly existing set of measured correlation matrices. As a most welcome side
effect, this approach drastically reduces the parameter dependence of the loss
distribution, allowing us to obtain very explicit results which show
quantitatively that the heavy tails prevail over diversification benefits even
for small correlations. We calibrate our random matrix model with market data
and show how it is capable of grasping different market situations.
Furthermore, we present numerical simulations for concurrent portfolio risks,
i.e., for the joint probability densities of losses for two portfolios. For the
convenience of the reader, we give an introduction to the Wishart random matrix
model.Comment: Review of a new random matrix approach to credit ris
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