Gaussian Correlation Research Articles

Reducing Uncertainty in EQ-5D Value Sets: The Role of Spatial Correlation.

Scoring algorithms for the EQ-5D-3L are constructed subject to a large degree of uncertainty (a credible interval width of 0.152, which is significant in comparison to the reported minimal important differences). The purpose of this work is to explore modeling techniques that will reduce the extent of this uncertainty. We used the US valuation study data. A Bayesian approach was used to calculate predicted utilities and credible intervals. A spatial Gaussian correlation structure was used to model correlation among health states (HS), thus allowing directly valued HS to contribute to the predicted utility of nearby unvalued HS. Leave-one-out cross-validation was used to compare model performances. The average posterior standard deviation was 0.039 for the unvalued health states and 0.011 for the valued health states. Using cross-validation, the US D1 model had 31% coverage probability. Models with independent and Gaussian correlation had coverage probabilities of 95% and 93%, respectively. Moreover, the Gaussian correlation structure resulted in a 25.6% reduction in mean squared error (SE) and 13.2% reduction in mean absolute error (AE) compared to the independent correlation structure (mean SE of 0.00131 v. 0.00176 and mean AE of 0.02818 v. 0.03248). Uncertainty was substantially lower for the directly valued HS compared to unvalued HS, suggesting direct valuation of as many health states as possible. Incorporation of a spatial correlation significantly reduced uncertainty. Hence, we suggest incorporating this when constructing scoring algorithms.

Reconciling Unevenly Sampled Paleoclimate Proxies: a Gaussian Kernel Correlation Multiproxy Reconstruction

Reconstructing past hydroclimatic variability using climate-sensitive paleoclimate proxies provides context to our relatively short instrumental climate records and a baseline from which to assess the impacts of human-induced climate change. However, many approaches to reconstructing climate are limited in their ability to address sampling variability inherent in different climate proxies. We iteratively optimise an ensemble of possible reconstruction data series to maximise the Gaussian kernel correlation of Rehfeld et al. (2011) which reconciles differences in the temporal resolution of both the target variable and proxies or covariates. The reconstruction method is evaluated using synthetic data with different degrees of sampling variability and noise. Two examples using paleoclimate proxy records and a third using instrumental rainfall data with missing values are used to demonstrate the utility of the method. While the Gaussian kernel correlation method is relatively computationally expensive, it is shown to be robust under a range of data characteristics and will therefore be valuable in analyses seeking to employ multiple input proxies or covariates.

Initial correlations of the Glasma energy-momentum tensor

We present an analytical calculation of the covariance of the energy-momentum tensor associated to the gluon field produced in ultra-relativistic heavy ion collisions at early times, the Glasma. This object involves the two-point and single-point correlators of the energy-momentum tensor (〈Tμν (x⊥)Tσρ(y⊥)〉 and 〈Tμν (x⊥)〉, respectively) at proper time τ = 0+. Our approach is based on the Color Glass Condensate effective theory, which allows us to map the fluctuations of the valence color sources in the colliding nuclei to those of the energy-momentum tensor of the produced gluon fields via the solution of the classical equations of motion in the presence of external currents. The color sources in the two colliding nuclei are characterized by Gaussian correlations, albeit in more generality than in the McLerran-Venugopalan model, allowing for non-trivial impact parameter and transverse dependence of the two-point correlator. We compare our results to those obtained under the Glasma Graph approximation, finding agreement in the limit of short transverse separations. However, important differences arise at larger transverse separations, where our result displays a slower fall-off than the Glasma Graph result (1/r2 vs. 1/r4 power-law decay), indicating that the color screening of the correlations in the transverse plane occurs at distances larger than 1/Qs by a logarithmic factor sensitive to the infrared. In the Glasma flux tube picture, this implies that the color domains are larger than originally estimated.

STATISTICAL DISTRIBUTION OF THE LAYERED ROUGH SURFACE INDEX (LRSI)

In this paper we determine the statistical distributions of the co-and cross-polarized Layered Rough Surface Index (LRSI) for three-dimensional layered structures with an arbitrary number of slightly rough interfaces illuminated by an electromagnetic plane wave. For infinite surface areas and Gaussian centered height distributions, we show within the framework of the first-order small perturbation method that the LRSI under a given observation direction is a random variable, whose statistical distribution is only function of two parameters. Contrary to the intensity ratio which follows a heavy-tailed distribution, the LRSI has finite mean and variance. For a structure air/clayey soil/rock, we analyze the influence of a snow layer upon the probability laws in the cases of Gaussian or exponential correlation functions.

Towards more realistic hypotheses for the information content analysis of cloudy/precipitating situations – Application to a hyperspectral instrument in the microwave

Information Content (IC) analysis can be used before an instrument is built to estimate its retrieval uncertainties and analyse their sensitivity to several factors. It is a very useful method to define/optimize satellite instruments. IC has shown its potential to compare instrument concepts in the infrared or the microwave. IC is based on some hypotheses such as the the Gaussian character of the radiative transfer (RT) and instrument errors, the first‐guess errors (Gaussian character, std and correlation structure), or the linearization of the RT around a first guess. These hypotheses are easier to define for simple atmospheric situations. However, even in the clear‐sky case, their complexity has never ceased to increase towards more realism, to optimize the assimilation of satellite measurements in numerical weather prediction (NWP) systems. In the cloudy/precipitating case, these hypotheses are even more difficult to define in a realistic way as many factors are still very difficult to quantify. In this study, several tools are introduced to specify more realistic IC hypotheses than the current practice. We focus on microwave observations as they are more pertinent for clouds and precipitation. Although not perfect, the proposed solutions are a new step towards more realistic IC assumptions of cloudy/precipitating scenes. A state‐dependence of the RT errors is introduced, the first‐guess errors have a more complex vertical structure, the IC is performed simultaneously on all the hydrometeors to take into account the contamination effect of the RT input uncertainties, and the IC is performed on a diversified set of cloudy/precipitating scenes with well‐defined hydrometeor assumptions. The method presented in this study is illustrated using the HYperspectral Microwave Sensor (HYMS) instrument concept with channels between 6.9 and 874 GHz (millimetre and sub‐millimetre regions). HYMS is considered as a potential next generation microwave sounder.

Revisiting the role of rainfall variability and its interactive effects with the built environment in urban dengue outbreaks

Dengue fever is a rapidly spreading mosquito-borne disease. Previous studies have shown that dengue vector mosquitoes are weather sensitive, and the effect of temperature on dengue transmission has been confirmed. However, associations between rainfall events and dengue incidence are not consistent, and few studies have addressed the roles of the magnitude and frequency of rainfall events in dengue transmission. Therefore, the purpose of this study was to differentiate the long-term and short-term effects of rainfall variation on dengue transmission and to investigate these effects within different socio-ecological contexts in southern Taiwan, which is a high-epidemic tropical region. A negative binomial multilevel model with Gaussian serial correlation was used in this study to investigate the intra- and inter-annual rainfall variability to determine the effects of rainfall on dengue occurrence in the pre-epidemic and epidemic seasons. Our significant results indicate that short-term rainfall and dengue occurrence show a non-linear relationship in which medium rainfall during the dengue season poses the most significant risk. We also found that rainfall effects are interactive to the percentage of old houses. Our results show strong synergistic interactions between low rain frequency and old house percentage, and between cumulative rainfall and old house percentage, contributing to dengue outbreaks. Our findings also differentiate the effects of short-term and long-term rainfall in old built-up environments on dengue occurrence. This implies that during rainy periods, old neighborhoods may require more attention from the public and private sectors to improve environmental quality and promote resident health.

Estimating and Testing Nonlinear Local Dependence Between Two Time Series

ABSTRACT The most common measure of dependence between two time series is the cross-correlation function. This measure gives a complete characterization of dependence for two linear and jointly Gaussian time series, but it often fails for nonlinear and non-Gaussian time series models, such as the ARCH-type models used in finance. The cross-correlation function is a global measure of dependence. In this article, we apply to bivariate time series the nonlinear local measure of dependence called local Gaussian correlation. It generally works well also for nonlinear models, and it can distinguish between positive and negative local dependence. We construct confidence intervals for the local Gaussian correlation and develop a test based on this measure of dependence. Asymptotic properties are derived for the parameter estimates, for the test functional and for a block bootstrap procedure. For both simulated and financial index data, we construct confidence intervals and we compare the proposed test with one based on the ordinary correlation and with one based on the Brownian distance correlation. Financial indexes are examined over a long time period and their local joint behavior, including tail behavior, is analyzed prior to, during and after the financial crisis. Supplementary material for this article is available online.

A Flexible Temporal Velocity Model for Fast Contaminant Transport Simulations in Porous Media

AbstractIn subsurface aquifers, dispersion of contaminants is highly affected by the heterogeneity of the hydraulic conductivity field. As an alternative to Monte Carlo simulations on probable conductivity fields, stochastic velocity processes have been introduced to assess the uncertainty in the transport of contaminants. In continuum‐scale simulations, discrete velocity models (such as correlated continuous time random walk) focus on modeling plume dispersion in the longitudinal direction. There are alternative continuous velocity processes (such as the polar Markovian velocity process [PMVP]) that are able to accurately model transport in both longitudinal and transverse directions. Importantly, the PMVP model correctly predicts the limited spreading of the ensemble contaminant plume in the transverse direction. However, the stochastic differential equations used in the PMVP model have specific drift and diffusion functions that are designed for the exponential correlation structure. In this paper, a new discrete velocity process is described that is applicable to modeling transport in two‐dimensional conductivity fields for both Gaussian and exponential correlation structures. This method is simple, in a sense that it does not require modeling the functional form of the drift and diffusion functions. The new method is validated against Monte Carlo simulations for both correlation structures with high variances of log conductivity.

Nonlinear reflection of weak shock waves from a rough surface in air

Irregular reflection of weak acoustic shock waves occurs under the framework of the von Neumann paradox. In this study, the influence of the surface roughness on the reflection pattern was studied experimentally using spark-generated spherically divergent N-waves of 1.4 cm length reflecting from rigid rough surfaces in air. Dimensions of the roughness were varied from 20 up to 500 μm for different surfaces. A Mach-Zehnder interferometry method was used to reconstruct the pressure waveforms near the surface. The reconstruction was performed by applying the inverse Abel transform to the phase of the signal measured by the interferometer. It was shown that the height of the Mach stem became shorter for surfaces with larger dimensions of the roughness and disappeared when the surface roughness was large enough. Such tendency was also observed in simulations based on the Euler equations where the acoustic source was introduced as a Gaussian-envelope energy injection and the roughness was either sinusoidal or random and described by a Gaussian correlation function. [Work supported by RSF-17-72-10277 and by the Labex CeLyA of Universite de Lyon, operated by the French National Research Agency (ANR-10-LABX-0060/ ANR-11-IDEX-0007).]Irregular reflection of weak acoustic shock waves occurs under the framework of the von Neumann paradox. In this study, the influence of the surface roughness on the reflection pattern was studied experimentally using spark-generated spherically divergent N-waves of 1.4 cm length reflecting from rigid rough surfaces in air. Dimensions of the roughness were varied from 20 up to 500 μm for different surfaces. A Mach-Zehnder interferometry method was used to reconstruct the pressure waveforms near the surface. The reconstruction was performed by applying the inverse Abel transform to the phase of the signal measured by the interferometer. It was shown that the height of the Mach stem became shorter for surfaces with larger dimensions of the roughness and disappeared when the surface roughness was large enough. Such tendency was also observed in simulations based on the Euler equations where the acoustic source was introduced as a Gaussian-envelope energy injection and the roughness was either sinusoidal or r...

Gaussian mixtures: Entropy and geometric inequalities

A symmetric random variable is called a Gaussian mixture if it has the same distribution as the product of two independent random variables, one being positive and the other a standard Gaussian random variable. Examples of Gaussian mixtures include random variables with densities proportional to $e^{-|t|^p}$ and symmetric $p$-stable random variables, where $p\in(0,2]$. We obtain various sharp moment and entropy comparison estimates for weighted sums of independent Gaussian mixtures and investigate extensions of the B-inequality and the Gaussian correlation inequality in the context of Gaussian mixtures. We also obtain a correlation inequality for symmetric geodesically convex sets in the unit sphere equipped with the normalized surface area measure. We then apply these results to derive sharp constants in Khintchine inequalities for vectors uniformly distributed on the unit balls with respect to $p$-norms and provide short proofs to new and old comparison estimates for geometric parameters of sections and projections of such balls.

Robust portfolio selection based on Gaussian rank correlation estimator

Estimating the covariance matrix of stock returns is a fundamental question in empirical finance with implications for portfolio selection. In the presence of outliers, classical estimates of covariance and correlation matrices are not reliable. For this reason, many robust estimator methods are given. However, high dimensional data poses great challenges to the traditional estimation, the merit of robust estimator cannot retain and improved robust estimator is required. In this paper, we proposed a robust pairwise covarinace matrix with Gaussian rank correlation, which is acting an input to Markowitz portfolio model. There are two main advantages of the proposed way. The first is that the final covariance estimator is positive semidefinite, we need not to transform the estimator. The second is that the covariance estimator can be computed fast because of the pairwise covariance and the Gaussian rank crrelation estimation. Moreover, our numerical results on empirical data show that the proposed estimation is much better than the traditional method. Through empirical studies, we also found that estimation error in sample mean should be considerd in Mean-variance portfolios.

Cut and join operator ring in tensor models

Recent advancement of rainbow tensor models based on their superintegrability (manifesting itself as the existence of an explicit expression for a generic Gaussian correlator) has allowed us to bypass the long-standing problem seen as the lack of eigenvalue/determinant representation needed to establish the KP/Toda integrability. As the mandatory next step, we discuss in this paper how to provide an adequate designation to each of the connected gauge-invariant operators that form a double coset, which is required to cleverly formulate a tree-algebra generalization of the Virasoro constraints. This problem goes beyond the enumeration problem per se tied to the permutation group, forcing us to introduce a few gauge fixing procedures to the coset. We point out that the permutation-based labeling, which has proven to be relevant for the Gaussian averages is, via interesting complexity, related to the one based on the keystone trees, whose algebra will provide the tensor counterpart of the Virasoro algebra for matrix models. Moreover, our simple analysis reveals the existence of nontrivial kernels and co-kernels for the cut operation and for the join operation respectively that prevent a straightforward construction of the non-perturbative RG-complete partition function and the identification of truly independent time variables. We demonstrate these problems by the simplest non-trivial Aristotelian RGB model with one complex rank-3 tensor, studying its ring of gauge-invariant operators, generated by the keystone triple with the help of four operations: addition, multiplication, cut and join.

Parametrization and Optimization of Gaussian Non-Markovian Unravelings for Open Quantum Dynamics.

We derive a family of Gaussian non-Markovian stochastic Schrödinger equations for the dynamics of open quantum systems. The different unravelings correspond to different choices of squeezed coherent states, reflecting different measurement schemes on the environment. Consequently, we are able to give a single shot measurement interpretation for the stochastic states and microscopic expressions for the noise correlations of the Gaussian process. By construction, the reduced dynamics of the open system does not depend on the squeezing parameters. They determine the non-Hermitian Gaussian correlation, a wide range of which are compatible with the Markov limit. We demonstrate the versatility of our results for quantum information tasks in the non-Markovian regime. In particular, by optimizing the squeezing parameters, we can tailor unravelings for improving entanglement bounds or for environment-assisted entanglement protection.

Conductivity and Transmissivity of a Single Fracture

The effective flow and conduction properties of fractures with Gaussian spatial correlations are investigated by solving the microscale governing equations in three-dimensional samples, along the lines initiated by Mourzenko et al. (J Phys II(5):465–482, 1995), Volik et al. (Trasnp Porous Media 27:305–325, 1997) but in greater details, over a wider range of the parameters, and with greatly improved accuracy. The effective transport coefficients are related to intrinsic geometrical characteristics, quantified by the mean aperture, the surface roughness RMS amplitude, its correlation length, and the intercorrelation coefficient of the roughness on the two surfaces. Extensive results are presented and analyzed. An empirical relationship between the transmissivity and conductivity is formulated, the validity of the Reynolds approximation is assessed, and heuristic expressions are proposed for the direct estimation of the transport coefficients as functions of the fracture geometrical characteristics.

Coherent pseudo-mode representation of partially coherent surface plasmon polaritons.

We develop a general coherent (pseudo)-mode representation of partially coherent surface plasmon polaritons in the Kretschmann excitation geometry. We obtain explicit analytical results for coherent pseudo-modes of narrowband SPPs with Gaussian spectra and spectral correlations. We also evaluate the global degree of coherence of such SPPs which quantifies their overall coherence state within a given spatial domain. Not only will the developed coherent pseudo-mode representation facilitate SPP coherence state characterization, but it will also substantially reduce the computational complexity of the studies of partially coherent SPP interactions with nanoparticles.

Continuous-variable supraquantum nonlocality

Supraquantum nonlocality refers to correlations that are more nonlocal than allowed by quantum theory but still physically conceivable in post-quantum theories, in the sense of respecting the basic no-faster-than-light communication principle. While supraquantum correlations are relatively well understood for finite-dimensional systems, little is known in the infinite-dimensional case. Here, we study supraquantum nonlocality for bipartite systems with two measurement settings and infinitely many outcomes per subsystem. We develop a formalism for generic no-signaling black-box measurement devices with continuous outputs in terms of probability measures, instead of probability distributions, which involves a few technical subtleties. We show the existence of a class of supraquantum Gaussian correlations, which violate the Tsirelson bound of an adequate continuous-variable Bell inequality. We then introduce the continuous-variable version of the celebrated Popescu-Rohrlich (PR) boxes, as a limiting case of the above-mentioned Gaussian ones. Finally, we perform a characterisation of the geometry of the set of continuous-variable no-signaling correlations. Namely, we show that that the convex hull of the continuous-variable PR boxes is dense in the no-signaling set. We also show that these boxes are extreme in the set of no-signaling behaviours and provide evidence suggesting that they are indeed the only extreme points of the no-signaling set. Our results lay the grounds for studying generalized-probability theories in continuous-variable systems.

An Improved BRISQUE Algorithm Based on Non-zero Mean Generalized Gaussian Model and Global Structural Correlation Coefficients

An Improved BRISQUE Algorithm Based on Non-zero Mean Generalized Gaussian Model and Global Structural Correlation Coefficients

Statistical Characteristics of the Gaussian-Noise Spikes Exceeding the Specified Threshold as Applied to Discharges in a Thundercloud

We obtain expressions for the probabilities of the normal-noise spikes with the Gaussian correlation function and for the probability density of the inter-spike intervals. As distinct from the delta-correlated noise, in which the intervals are distributed by the exponential law, the probability of the subsequent spike depends on the previous spike and the interval-distribution law deviates from the exponential one for a finite noise-correlation time (frequency-bandwidth restriction). This deviation is the most pronounced for a low detection threshold. Similarity of the behaviors of the distributions of the inter-discharge intervals in a thundercloud and the noise spikes for the varying repetition rate of the discharges/spikes, which is determined by the ratio of the detection threshold to the root-mean-square value of noise, is observed. The results of this work can be useful for the quantitative description of the statistical characteristics of the noise spikes and studying the role of fluctuations for the discharge emergence in a thundercloud.

Relationship between oil price and exchange rate by FDA and copula

ABSTRACTThis article investigates the relationship between daily crude oil prices and exchange rates. Functional data analysis is used to show the clustering pattern of exchange rates and oil prices over the time period through high dimensional visualizations. We select exchange rates for important currencies related to crude oil prices by using the objective Bayesian variable selection method. The selected sample data exhibits non-normal distribution with fat tails and skewness. Under the non-normality of the return series, we use copula functions that do not require to assume the bivariate normality to consider marginal distribution. In particular, our study applies the popular and powerful statistical methods such as Gaussian copula partial correlations and Gaussian copula marginal regression. We find evidence of significant dependence for all considered pairs, except for the Mexican peso-Brent. Our empirical results also show that the rise in the West Texas Intermediate (WTI) oil price returns is associated with a depreciation of the US dollar.

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.