Gaussian Correlation Model Research Articles

Wealth management: Modeling the nonlinear dependence

This work aims at the development of an enhanced portfolio selection method, which is based on the classical portfolio theory proposed by Markowitz (1952) and incorporates the local Gaussian correlation model for optimization. This novel method of portfolio selection incorporates two assumptions: the non-linearity of returns and the empirical observation that the relation between assets is dynamic. By selecting ten assets from those available in Yahoo Finance from S&P500, between 1985 and 2015, the performance of the new proposed model was measured and compared to the model of portfolio selection of Markowitz (1952) . The results showed that the portfolios selected using the local Gaussian correlation model performed better than the traditional Markowitz (1952) method in 63% of the cases using block bootstrap and in 71% of the cases using the standard bootstrap. Comparing the calculated Sharpe ratios, the proposed model yielded a better adjusted risk-return in the majority of the cases studied.

Implementation of Region-Based Covariance Localization Ensemble Kalman Filter in History Matching Workflow

Background:History matching is an indispensable phase in the workflow of reservoir analysis. Nevertheless, there is a considerable challenge in performing the procedure in a proper scientific manner due to the inherent nature of non-unique solutions from the many-unknown variables with limited known equations.Objective:In this study, we introduce the Ensemble Kalman Filter (EnKF) method complemented by the Region-Based Covariance Localization (RCL) scheme to address the aforementioned issue.Method:The algorithms work initially by modifying the covariance localization generated by Gaussian correlation model using region information such as facies or flow unit, in which the area within a region is spatially correlated. Subsequently, the correlation between distant areas in the region is eliminated, hence promoting better modification of the distribution of the parameters while maintaining the characteristics of the predefined geological model of the reservoir.Result:Result shows that RCL scheme is capable of enhancing the performance of EnKF procedure and produce parameter distributions that is close to the true model of the reservoir.Conclusion:Implementation of the proposed methodology ameliorates the accuracy and reliability of the history matching process, thus establishing better consideration in predicting reservoir performance.

Correlated Differential Privacy Protection for Mobile Crowdsensing

Mobile CrowdSensing (MCS) is a new paradigm that leverages pervasive mobile devices to efficiently collect the big sensory data, enabling various large-scale applications. However, people’s concerns about the loss of individual privacy seriously hinder the prevalence of MCS applications. Differential privacy is widely focused owing to its rigorous definition and strong privacy guarantee, but the state-of-the-art studies still demonstrate its weakness on correlated data, resulting in compromising individual privacy. In this paper, we investigate the influence of sensing data correlation on differential privacy protection for MCS systems, and explore the perturbation mechanisms from two different perspectives. From a protector’s perspective, based on the Bayesian Network to model the probabilistic relationship among sensing data, we use the classical definition of differential privacy to deduce the scale parameter, and present one perturbation mechanism. From an adversary’s perspective, based on the Gaussian correlation model to describe the data correlation, we analyze the importance of the maximum correlated group to compute the Bayesian differential privacy leakage, and then provide another perturbation mechanism. Compared with the existing solutions, our mechanisms are applicable to arbitrary aggregate query function, and can avoid introducing too much noise. Moreover, we demonstrate the effectiveness of our mechanisms through extensive simulations.

Laser speckle contrast imaging is sensitive to advective flux.

Unlike laser Doppler flowmetry, there has yet to be presented a clear description of the physical variables that laser speckle contrast imaging (LSCI) is sensitive to. Herein, we present a theoretical basis for demonstrating that LSCI is sensitive to total flux and, in particular, the summation of diffusive flux and advective flux. We view LSCI from the perspective of mass transport and briefly derive the diffusion with drift equation in terms of an LSCI experiment. This equation reveals the relative sensitivity of LSCI to both diffusive flux and advective flux and, thereby, to both concentration and the ordered velocity of the scattering particles. We demonstrate this dependence through a short series of flow experiments that yield relationships between the calculated speckle contrast and the concentration of the scatterers (manifesting as changes in scattering coefficient), between speckle contrast and the velocity of the scattering fluid, and ultimately between speckle contrast and advective flux. Finally, we argue that the diffusion with drift equation can be used to support both Lorentzian and Gaussian correlation models that relate observed contrast to the movement of the scattering particles and that a weighted linear combination of these two models is likely the most appropriate model for relating speckle contrast to particle motion.

A simulation study on the quantitative assessment of tissue microstructure with photoacoustics.

A detailed derivation of a quantity, defined as the acoustic power per unit solid angle far from the illuminated volume divided by the intensity of the incident light beam and termed as differential photoacoustic (PA) cross section, is presented. The expression for the differential PA cross section per unit absorbing volume retains two terms, namely, the coherent and the incoherent parts. The second part based on a correlation model can be employed to analyze the PA signal power spectrum for tissue characterization. The performances of the fluid sphere, Gaussian, and exponential correlation models in assessing the mean size and the variance in the optical absorption coefficients of absorbers were investigated by performing in silico experiments. It was possible to evaluate diameters of solid spherical absorbers with radii ≥ 20 μm with an accuracy of 10% for an analysis bandwidth of 5 to 50 MHz using the first two correlation models. The accuracy of estimation was about 22% for fluid spheres mimicking erythrocytes for the third correlation model for an analysis bandwidth of 5 to 100 MHz. The extracted values of average variance in the optical absorption coefficients demonstrated good correlation with the nominal values. This study suggests that the method presented here may be developed as a potential tissue characterization tool.

On the condition number anomaly of Gaussian correlation matrices

Spatial correlation matrices appear in a large variety of applications. For example, they are an essential component of spatial Gaussian processes, also known as spatial linear models or Kriging estimators, which are powerful and well-established tools for a multitude of engineering applications such as the design and analysis of computer experiments, geostatistical problems and meteorological tasks.In radial basis function interpolation, Gaussian correlation matrices arise frequently as interpolation matrices from the Gaussian radial kernel function. In the field of data assimilation in numerical weather prediction, such matrices arise as background error covariances.Over the past thirty years, it was observed by several authors from several fields that the Gaussian correlation model is exceptionally prone to suffer from ill-conditioning, but a quantitative theoretical explanation for this anomaly was lacking. In this paper, a proof for the special position of the Gaussian correlation matrix is given. The theoretical findings are illustrated by numerical experiment.

Substitution Costs in Managed Synthetic CDOs

Managed synthetic CDOs permit the dynamic substitution of credits in the reference portfolio. The expectation of investors in is that a skilled manager should be able to identify deteriorating credits before they experience a credit event and should therefore be able to remove the credit from the portfolio at a lower cost than the loss due to a credit event. This ability to substitute credits has a cost and in this paper we explain the source of this cost and calculate it across a wide range of CDO deal scenarios using a Gaussian copula correlation model. In deals where the cost is transformed into a change in subordination, we show that in it is possible to estimate this change without use of a correlation model. We also describe an extension of Vasicek's portfolio model that allows us to improve upon this estimate. We also incorporate the effect of transaction costs into the substitution cost and calculate their size across a range of CDO parameters. Our aim is to enhance transparency around the cost of substitutions.

Moving Kriging reconstruction for high-order finite volume computation of compressible flows

This paper describes the development of a high-order finite volume method for the solution of compressible viscous flows on unstructured meshes. The novelty of this approach is based on the use of moving Kriging shape functions for the computation of the derivatives in the numerical flux reconstruction step at the cell faces. For each cell, the successive derivatives of the flow variables are deduced from the interpolation function constructed from a compact stencil support for both Gaussian and quartic spline correlation models. A particular attention is paid for the study of the influence of the correlation parameter onto the accuracy of the numerical scheme. The effect of the size of the moving Kriging stencil is also investigated. Robustness and convergence properties are studied for various inviscid and viscous flows. Results reveal that the moving Kriging shape function can be considered as an interesting alternative for the development of high-order methodology for complex geometries.

Comparing alternative Lévy base correlation models for pricing and hedging CDO tranches

In this paper we investigate alternative Lévy base correlation models that arise from the Gamma, Inverse Gaussian and CMY distribution classes. We compare these models with the basic (exponential) Lévy base correlation model and the classical Gaussian base correlation model. For all investigated models, the Lévy base correlation curve is significantly flatter than the corresponding Gaussian curve, which indicates better correspondence of the Lévy models with reality. Furthermore, we present the results of pricing bespoke tranchlets and comparing deltas of both standard and custom-made tranches under all the considered models. We focus on deltas with respect to the CDS index and individual CDSs, and the hedge ratio for hedging the equity tranche with the junior mezzanine.

Gaussian process method for form error assessment using coordinate measurements

A Gaussian process method for modeling and assessing form errors is presented. The Gaussian process method decomposes a geometric feature into three components: designed geometric form, systematic manufacturing errors and random manufacturing errors. It models the systematic manufacturing errors as a spatial model using a Gaussian correlation function and models the random manufacturing errors as independent identically distributed noises. Based on a handful of coordinate measurements, the Gaussian process model reconstructs the part surface and assesses the form error better than traditional methods. The Gaussian process method also provides an empirical distribution of the form error, allowing engineers to quantify the decision risk on part acceptance. This method works for generic geometric features. The method is implemented on two common features: a straight and a round feature. Simulated datasets as well as actual coordinate measuring machine data are used to demonstrate the improvement achieved by the proposed method over the traditional approaches.

Pricing Distressed CDOs with Base Correlation and Stochastic Recovery

In February and March 2008 it was temporarily not possible to calibrate the standard Gaussian Base correlation model to the complete set of CDX.IG and ITRAXX.IG CDO tranche quotes. For instance, in CDX.IG it failed for the 15%-30% senior tranche and hence the sucessive 30%-100% tranche. The reason is that the Gaussian Base correlation model was not able to generate enough probability for high portfolio losses, while preserving the calibration to mezzanine and equity tranches. We introduce a Gaussian Base correlation model with correlated stochastic recovery rates to overcome this problem. Moreover, our model can be used to price super senior tranches (e.g. 60%-100%), which have a fair spread of zero in a standard copula model with fixed recovery.

Spatial resolution enhancement/smoothing of stereo–particle-image-velocimetry data using proper-orthogonal-decomposition–based and Kriging interpolation methods

Methods for data reconstruction and spatial enhancement of experimental data for a transitional boundary layer with laminar separation bubble are investigated. Particularly, proper orthogonal decomposition (POD) is applied to direct numerical simulation (DNS) data to extract the DNS-based POD modes, which are projected onto the experimental data (via a least-squares procedure) in order to obtain model coefficients. These model coefficients are then used to reconstruct, “interpolate,” and smooth the experimental data based on the DNS modes. In addition, in order to compare and assess the effectiveness of the present DNS-based procedure, Kriging interpolation is performed on the experimental (as well as numerical) data. These procedures are applied to time periodic (experimental) instantaneous spanwise vorticity (ωz) at a constant spanwise location. We have demonstrated that particle-image-velocimetry (PIV)-based POD modes can be smoothed by Kriging interpolation, thus a noise-free reconstruction of PIV data can be achieved. It is also found that for very low resolution experimental data, DNS-based interpolation is superior over Kriging interpolation. On the other hand, Kriging interpolation based on the Gaussian correlation model works very well for sufficiently high resolution experimental data. The correlation parameter can be used to control the degree of smoothness in the data reconstruction. Both procedures effectively eliminate the unwanted noise in the experimental data. One important difference between the two procedures is that, with quite some confidence, the DNS-based procedure can also be used for “extrapolation” since the model coefficients do not depend on spatial variation. In fact, we show that near-wall spanwise vorticity, which is not available from experimental data, can be recovered faithfully. Moreover, the enhancement (interpolation and smoothing) of full three-dimensional PIV data has been performed by Kriging interpolation employing a Gaussian correlation model.

Surface Electron Transport over a Liquid-Helium Film Covering a Smooth Solid Substrate

The mobility of surface electrons localized over a superfluid helium film covering a solid substrate is calculated by taking into account the essential scattering processes of electrons by helium atoms, by ripplons and by the helium-substrate interface roughness. The last scattering process dominates for thin helium films with thickness with d ≲ 10−6 cm. A new scattering Hamiltonian, recently derived by the method of image forces, is employed. The calculated results for the mobility are compared with experimental data by fitting the two characteristic sizes of the Gaussian correlation model for surface defects. The agreement is rather good in the case of a glass substrate.

Measurement and data processing approach for detecting anisotropic spatial statistics of the turbulence-induced index of refraction fluctuations in the upper atmosphere.

We discuss a method of data reduction and analysis that has been developed for a novel experiment to detect anisotropic turbulence in the tropopause and to measure the spatial statistics of these flows. The experimental concept is to make measurements of temperature at 15 points on a hexagonal grid for altitudes from 12,000 to 18,000 m while suspended from a balloon performing a controlled descent. From the temperature data, we estimate the index of refraction and study the spatial statistics of the turbulence-induced index of refraction fluctuations. We present and evaluate the performance of a processing approach to estimate the parameters of an anisotropic model for the spatial power spectrum of the turbulence-induced index of refraction fluctuations. A Gaussian correlation model and a least-squares optimization routine are used to estimate the parameters of the model from the measurements. In addition, we implemented a quick-look algorithm to have a computationally nonintensive way of viewing the autocorrelation function of the index fluctuations. The autocorrelation of the index of refraction fluctuations is binned and interpolated onto a uniform grid from the sparse points that exist in our experiment. This allows the autocorrelation to be viewed with a three-dimensional plot to determine whether anisotropy exists in a specific data slab. Simulation results presented here show that, in the presence of the anticipated levels of measurement noise, the least-squares estimation technique allows turbulence parameters to be estimated with low rms error.

Settling statistics of hard sphere particles.

Direct imaging of settling, non-Brownian, hard sphere, particles allows measurement of particle occupancy statistics as a function of time and sampling volume dimension. Initially random relative particle number fluctuations, <N2-<N>(2)>/<N> = 1, become suppressed, anisotropic, and <N> dependent. Fitting to a simple Gaussian pair correlation model suggests a minute long ranged correlation leads to strong if not complete suppression of number fluctuations. Calflisch and Luke predict a divergence in velocity fluctuations with increasing sample volume size based on random (Poisson) statistics. Our results suggest this is not a valid assumption for settling particles.

THEORY AND EXPERIMENT FOR THE CHARACTERIZATION OF RANDOM SURFACES BY THE AVERAGE INTENSITY OF IMAGE SPECKLES OF VARIABLE APERTURES

Using the Gaussian correlation model of random surfaces, we conduct the theoretical derivation of the image-plane intensity produced by a weak scatterer in the 4f optical filtering system.Then the method is proposed for characterizing the square-root-mean deviation roughness and lateral correlation length.This method uses the derived theoretical expressions to fit the experimentally measured curve of image speckle intensity versus the radius of filtering aperture,and the two surface parameters can be extracted simultaneously.In the experiment,random surface samples are specially made and their surface parameters are measured. The results conforms with those obtained by atomic force microscopy,which shows that the method of this paper is of good accuracy.

Error bounds on ultrasonic scatterer size estimates

Precision errors that occur in estimating the average scatterer size from pulse-echo ultrasound waveforms are examined in detail. The method-independent lower bound on estimation error is found from the Cramér-Rao inequality for comparison with the predicted error for the measurement technique currently used to estimate scatterer sizes in soft biological tissues. The probability density function for the estimate is also derived. From these statistical analyses, strategies for designing experiments that minimize the error are discussed. It is shown that compared with biological variability, measurement errors in scatterer size estimates are relatively large. Consequently, there is reason to continue searching for more efficient estimators. Although the analysis and results are derived for Gaussian correlation models that have been used to study the function and structure of kidneys, generalization to include correlation models for other tissues is straightforward.

Cross correlations and cross spectra for spaced antenna wind profilers: 1. Theoretical analysis

The presented theory ties the properties of a turbulently advected scattering medium to the cross correlation and cross spectrum of signals in a general configuration of receiving and transmitting antennas. The correlation length of Bragg scatterers and antenna diameter are the significant parameters determining the diffraction pattern's correlation length. We examine how vertical anisotropy of the scattering medium affects the diffraction pattern's correlation length. We demonstrate that the cross spectrum can be formulated in terms of a pair of spectral sampling functions (a one‐dimensional Doppler and a three‐dimensional wavenumber function), and closed form solutions are obtained. We give the conditions under which the scattering medium's statistical properties can be represented by a Gaussian correlation or spectral model, and the distance over which the diffraction pattern simply advects without significant change. We show that the diffraction pattern of a pair of scatterers can translate at the speed of the scatterers, not twice their speed as is commonly thought.

Small-angle x-ray scattering of isotactic polystyrene

Isothermal crystallization process of isotactic polystyrene at 167°C has been studied by smallangle x-ray scattering. The observed SAXS intensities consist of the twophase lamellar structure component, the density fluctuation, and the foreign particle components. The profile of lamellar structure component remains unchanged during crystallization while its intensity increases with crystallization. The lamellar structure of isotactic polystyrene is investigated on the basis of the interface distribution function. An interface distribution function is obtained from the lamellar structure component after correcting the effect of the finite thickness of boundary regions between crystalline and amorphous phases. In order to obtain the structure parameters, the “Gaussian correlation model” is used, in which the correlation between the distributions of neighboring crystal and amorphous thicknesses is taken into account. Agreement is satisfactory between the experimental results and the calculations. The structure parameters of isotactic polystyrene are determined for isothermal crystallization at 167°C as follows: the average and the standard deviation of crystal thickness are 40 A and 10 A, respectively, those of amorphous thickness are 70 A and 23 A, and the standard deviation of long period is 31 A.

Two-Dimensional NMR Characterization of Local Structure in Two Polystyrene Blends

Solid-state NMR spin diffusion measurements have been used to investigate the local structures in two miscible polymer systems, the isotopic polystyrene blend PS-d 5 /PS-d 3 and poly(2,6-dimethylphenylene oxide)(PPO)/PS-d 3 . The experimental spin diffusion build-up curves were compared with theoretical ones based on a number of structural models. It was found that a Gaussian correlation model furnished the best agreement with the experimental data, and this implies the existence of some short-range ordering in the local environment in such nominally miscible blend systems. The best fit of the spin diffusion curves gave a correlation length of 0.5-0.6 nm for the PS-d 5 /PS-d 3 blends and 0.4 nm for the PPO/PS-d 3 blends