Higher-order Moments Research Articles

Exact Moments of Residuals of Independence

The diagnosis of residuals of independence is critical in association analysis and loglinear modeling of two-way contingency tables. Most residual diagnostics depend on large-sample methods, and diagnostic results become dubious when sample sizes are small or data are sparse. In such cases, statistical inference based on non-asymptotic theory or exact inference is desirable. This paper explicitly derives the first four moments of the residuals of independence in a two-way contingency table under a multinomial model. These exact moments are necessary tools for studying the analytical features of the distribution of residuals of independence, such as skewness and kurtosis. Higher-order moments can be found similarly, but the results are more complicated.

High order moment conserving method of classes in CFD code

Abstract Dispersed multiphase flows are widely present in the majority of chemical process industry equipment. For the purpose of design, optimization, and scale up of these industrial systems, robust, accurate and fast simulation methods are needed, especially when coupling computational fluid dynamics (CFD) with population balance models (PBM). In this work, the high-order moment conserving method of classes (HMMC) is implemented and tested within the commercial CFD software of ANSYS Fluent with two simple well-defined test cases and a realistic 3D simulation of rotating disc (RDC) extractor. Firstly, a zero-dimensional PBM with well-mixed assumption and no convection was solved for a single computational cell in Fluent to verify the implementation in comparison with a simple reactor model in MATLAB. Secondly, the convection was considered by solving a one-dimensional PBM for three computational cells side by side in Fluent and compared with an equivalent three staged reactor model in MATLAB. Eventually, realistic 3D RDC simulations were conducted to fully couple the HMMC and CFD in Fluent. The implementation of HMMC was compared to predictions with other state-of-the-art PBM solution methods, e.g., the quadrature method of moments (QMOM) and the fixed pivot technique (FPT) in Fluent and MATLAB platforms. The implementation of the HMMC in Fluent platform was straightforward with no additional challenges. The verification shows that the HMMC approach is robust and efficient for polydispersed multiphase CFD simulations.

A gradient-enhanced univariate dimension reduction method for uncertainty propagation

The univariate dimension reduction (UDR) method stands as a way to estimate the statistical moments of the output that is effective in a large class of uncertainty quantification (UQ) problems. UDR's fundamental strategy is to approximate the original function using univariate functions so that the UQ cost only scales linearly with the dimension of the problem. Nonetheless, UDR's effectiveness can diminish when uncertain inputs have high variance, particularly when assessing the output's second and higher-order statistical moments. This paper proposes a new method, gradient-enhanced univariate dimension reduction (GUDR), that enhances the accuracy of UDR by incorporating univariate gradient function terms into the UDR approximation function. Theoretical results indicate that the GUDR approximation is expected to be one order more accurate than UDR in approximating the original function, and it is expected to generate more accurate results in computing the output's second and higher-order statistical moments. Our proposed method uses a computational graph transformation strategy to efficiently evaluate the GUDR approximation function on tensor-grid quadrature inputs, and use the tensor-grid input-output data to compute the statistical moments of the output. With an efficient automatic differentiation method to compute the gradients, our method preserves UDR's linear scaling of computation time with problem dimension. Numerical results show that the GUDR is more accurate than UDR in estimating the standard deviation of the output and has a performance comparable to the method of moments using a third-order Taylor series expansion.

Experimental investigation of the flow disturbance near the trailing edge of slotted and non-slotted blades using skewness and kurtosis

The present study conducts an experimental investigation into the flow characteristics over a cascade of both slotted and non-slotted compressor blades. The focus is on evaluating potential statistical correlations between higher-order moments of velocity fluctuations, including Skewness and Kurtosis. The linear axial cascade comprises three NACA6409 blades, which are tested in both normal and slotted blade. Data acquisition was conducted using a hot wire anemometer at three measurement stations within the cascade. The hot wire sensor was positioned at distances of x/c = 0.125, 0.25, and 0.5 from the trailing edge (x), where x represents the distance from the probe to the trailing edge of the airfoil and (c) is the chord length of the blade. Measurements were taken at a blade angle of attack of 0° and two Reynolds numbers: 22,750 and 45,500. Results indicate that blade grooving enhances flow velocity, postpones separation and improves flow control in the trailing edge region. By comparing calculated Skewness and Kurtosis values with those predicted by existing boundary layer and free jet relations, more consistent correlations were identified. To provide more accurate relationships, two polynomials of the second and third order have been used. It was found that high-order values of velocity were obtained more accurately with the relations presented in this research. Although the accuracy of these predictions is significantly reduced in the proportion of larger distances. In distant stations, the loss velocity has decreased. As the distance from the model increases, the amount of inhomogeneities in the sequence increases and the values of the opposite Skewness become zero. Turbulence intensity has been reduced by slotting the blades.

Demand Risks and Term Structure of Volatility Index Futures

In this paper, we develop an equilibrium framework to explain the characteristics of volatility index (VIX) futures prices and returns across maturities. In the framework, the investors prefer VIX futures with specific maturities, and the arbitrageurs optimize portfolios based on mean-variance preferences. The model-implied futures prices are affected by the variance and demand risk factors. Theoretical and empirical analyses show that incorporating jump risks helps to explain the higher-order moments of futures and that including the demand factor improves futures pricing performance.

Improving the estimate of higher-order moments from lidar observations near the top of the convective boundary layer

Abstract. Ground-based lidar data have proven extremely useful for profiling the convective boundary layer (CBL). Many groups have derived higher-order moments (e.g., variance, skewness, fluxes) from high-temporal-resolution lidar data using an autocovariance approach. However, these analyses are highly uncertain near the CBL top when the depth of the CBL (zi) is changing during the analysis period. This is because the autocovariance approach is usually applied to constant height levels and the character of the eddies is changing on either side of the changing CBL top. Here, a new approach is presented wherein the autocovariance analysis is performed on a normalized height grid, with a temporally smoothed zi. Output from a large eddy simulation model demonstrates that deriving higher-order moments from time series on a normalized height grid has better agreement with the slab-averaged quantities than the moments derived from the original height grid.

Higher-order moments spillovers among energy, carbon and tourism markets: Time- and frequency-domain evidence.

This paper uses the GJRSK model to estimate the high-order moments of energy (oil, natural gas, and coal), the carbon market, and tourism stocks. Then, it utilizes a novel TVP-VAR time-frequency connectedness approach to examine higher-order moments spillovers among them. The results show a strong connectedness among the three markets. The energy market is the emitter of volatility, skewness and kurtosis spillovers; tourism stock is the receiver; and the carbon market is the transmitter. From a time-domain perspective, the higher-order moments spillovers of the three markets are time-varying, especially during extreme periods, where the energy market's spillover effects on tourism stocks are significantly enhanced, indicating that tourism stocks bear a greater risk at leptokurtosis and fat-tail moment. From a frequency-domain perspective, the long-term asymmetric spillovers of oil, natural gas, and tourism markets on the carbon market are more pronounced than the short-term. Moreover, the COVID-19 pandemic exacerbated the higher-moment spillovers of energy and tourism stocks on the carbon market. Meanwhile, the Russia-Ukraine conflict led to extreme risk transmission within the energy market. These findings have significant implications for cross-industry investors and green finance risk management.

Uniform inference in linear error-in-variables models: Divide-and-conquer

. It is customary to estimate error-in-variables models using higher-order moments of observables. This moments-based estimator is consistent only when the coefficient of the latent regressor is assumed to be nonzero. We develop a new estimator based on the divide-and-conquer principle that is consistent for any value of the coefficient of the latent regressor. In an application on the relation between investment, (mismeasured) Tobin’s q and cash flow, we find time periods in which the effect of Tobin’s q is not statistically different from zero. The implausibly large higher-order moment estimates in these periods disappear when using the proposed estimator.

Closure equationand higher-order moment relations in the Gauss-Hermite lattice Boltzmann method.

Moment methods are often used to solve transport problems involving the Boltzmann-BGK equation. Because the moment equationsare underdetermined, these methods require an additional "closure equation" that relates higher to lower-order moments. Here, we examine the closure equationand higher-order moment relations implicit in the lattice Boltzmann method (LBM) that use Gauss-Hermite quadrature for their discrete velocity sets. It is shown that the discrete-velocity-set itself defines the closure equationand higher-order moment relations, the precise forms of which are yet to be reported. The general formula we present facilitates the efficient computational evaluation of higher-order moments and provides insight into the operation of LBM that is anticipated to be useful in theoretical analyses of its performance. Derived formulas for two different velocity sets are validated against numerical implementations of the LBM for steady Couette flow.

Electron Influence on the Parallel Proton Firehose Instability in 10-moment, Multifluid Simulations

Instabilities driven by pressure anisotropy play a critical role in modulating the energy transfer in space and astrophysical plasmas. For the first time, we simulate the evolution and saturation of the parallel proton firehose instability using a multifluid model without adding artificial viscosity. These simulations are performed using a 10-moment, multifluid model with local and gradient relaxation heat-flux closures in high-β proton–electron plasmas. When these higher-order moments are included and pressure anisotropy is permitted to develop in all species, we find that the electrons have a significant impact on the saturation of the parallel proton firehose instability, modulating the proton pressure anisotropy as the instability saturates. Even for lower β's more relevant to heliospheric plasmas, we observe a pronounced electron energization in simulations using the gradient relaxation closure. Our results indicate that resolving the electron pressure anisotropy is important to correctly describe the behavior of multispecies plasma systems.

The VIRUS-dE Survey. I. Stars in Dwarf Elliptical Galaxies—3D Dynamics and Radially Resolved Stellar Initial Mass Functions

We analyze the stellar structure of a sample of dwarf ellipticals (dEs) inhabiting various environments within the Virgo cluster. Integral-field observations with a high spectral resolution allow us to robustly determine their low-velocity dispersions (∼25 km s−1) and higher-order kinematic moments out to the half-light radius. We find the dEs exhibit a diversity in ages, with the younger dEs being less enhanced than the older, suggesting a complex star formation history for those dEs that recently entered Virgo, while others have been quenched shortly after reionization. Orbit-superposition modeling allowed us to recover viewing angles, stellar mass-to-light ratios (with gradients), as well as the intrinsic orbit structure. We find that the angular momentum of the dEs is strongly suppressed compared to ordinary early-type galaxies and correlates with the environment. Flattened dEs are so because of a suppressed kinetic energy perpendicular to their equatorial plane. Combining population and dynamical modeling results, we find an age-dependent stellar initial mass function or, alternatively, evidence for a more extended star formation history for those galaxies that have had higher initial mass and/or inhabited lower-density environments. dEs appear to have a spatially homogeneous stellar structure, but the state they were “frozen” in as they stopped forming stars varies dramatically according to their initial conditions.

Revisiting each fracture size and spatial pattern: Inference from rock mass surface to interior

Estimating fracture size is a fundamental aspect of rock engineering. However, determining the most probable diameter (MPD) from a fracture’s surface trace remains challenging in the scientific community. The prevailing methodologies typically infer statistical distributions of fracture sizes rather than specific values. This research presents a novel approach to inferring the MPD and the true spatial distribution pattern of each fracture. The challenge lies in linking the inference process with the trace length of each fracture and the statistical characteristics of the entire outcrop. Additionally, it is necessary to address the non-unique inverse problem. The methodology comprises several key steps. Firstly, the issue of censoring bias is addressed by considering the lengths of the traces contained. Secondly, the orientation bias is corrected using the vector method, and the true mean trace length and standard deviation are estimated and derived. Thirdly, assuming a lognormal distribution for fracture sizes, the mean and standard deviation of diameters are derived through a high-order moment relationship between trace lengths and diameters, validated by Crofton’s theorem. Finally, the MPDs of all trace samples are determined by relating MPDs to trace lengths and the standard deviation of diameters using stereology techniques. Furthermore, the true fracture spatial patterns are inverted based on spatial geometric relationships. The proposed methodology is validated through rigorous Monte Carlo simulation and applied in a practical engineering case study, demonstrating its potential for use in rock engineering applications.

Diffusion and Spectroscopy of H2 in Myoglobin

The diffusional dynamics and vibrational spectroscopy of molecular hydrogen (H2) in myoglobin (Mb) is characterized. Hydrogen has been implicated in a number of physiologically relevant processes, including cellular aging or inflammation. Here, the internal diffusion through the protein matrix was characterized, and the vibrational spectroscopy was investigated using conventional empirical energy functions and improved models able to describe higher-order electrostatic moments of the ligand. Depending on the energy function used, H2 can occupy the same internal defects as already found for Xe or CO (Xe1 to Xe4 and B-state). Furthermore, four additional sites were found, some of which had been discovered in earlier simulation studies. Simulations using a model based on a Morse oscillator and distributed charges to correctly describe the molecular quadrupole moment of H2 indicate that the vibrational spectroscopy of the ligand depends on the docking site it occupies. This is consistent with the findings for CO in Mb from experiments and simulations. For H2, the maxima of the absorption spectra cover ∼20 cm−1 which are indicative of a pronounced Stark effect of the surrounding protein matrix on the vibrational spectroscopy of the ligand. Electronic structure calculations show that H2 forms a stable complex with the heme iron (stabilized by ∼−12 kcal/mol), but splitting of H2 is unlikely due to a high activation energy (∼50 kcal/mol).

Quantitative estimation of optical properties in bilayer media within the subdiffusive regime using a tilted fiber-optic probe in diffuse reflectance spectroscopy, part 1: a theoretical framework for designing probe geometry.

As biological tissues are highly heterogeneous, there is a great interest in developing non-invasive optical approaches capable of characterizing them in a very localized manner. Obtaining accurate absolute values of the local optical properties from the measured reflectance requires finding a probe geometry, which allows us to solve this inverse problem robustly and reliably despite neglecting the higher-order moments of the scattering phase function. Our goal is to develop a theoretical framework for designing tilted-fiber diffuse reflectance probes that allow quantitative estimation of the optical properties corresponding to limited tissue volume (typically a few cubic millimeters). Relationships among probe geometry, sampled tissue volume, and robustness of the inverse solver to calculate optical properties from reflectance are studied using Monte Carlo simulations. The analysis of the number of scattering events of the collected photons leads to the establishment of relationships among the probe geometry, the sampled tissue volume, and the validity of a subdiffusive regime for the reflectance. A methodology is proposed for the design of new compact probes with tilted fiber geometry that can quantitatively estimate the values of the optical coefficients in a localized manner within living biological tissues by recording diffuse reflectance spectra.

Higher-order moments of the Mott-Smith shock approximation

Higher-order moments of the Mott-Smith shock approximation

Study of net-baryon higher moments in PNJL model and their expectation for net-proton using the subensemble acceptance method for the search of QCD critical point

The critical point is one of the most important aspects of the QCD phase diagram of strongly interacting matter. The nonmonotonic behavior of the higher-order moments of conserved quantities like net-baryon (ΔB), net-charge (ΔQ), and net-strangeness (ΔS) are believed to be the signatures of the QCD critical point as a function of energy. We study the effect of the QCD critical point on moments of net-baryon in the Polyakov loop enhanced Nambu-Jona-Lasinio (PNJL) model of QCD with six-quark and eight-quark interactions for finite and infinite volume systems. The study is performed at energies similar to Relativistic Heavy-Ion Collider beam energy scan. Experimentally measuring conserved quantities is difficult due to systematic limitations. Therefore, net-proton, net-pion, and net-kaon are measured as the proxy of ΔB, ΔQ, and ΔS. Recent studies in the subensemble acceptance method on the hadron resonance gas (HRG) model show the dependency of the measured higher-order moment on the experimental acceptance. We applied the subensemble acceptance method to analyze the behavior of κσ2 of net-baryon distribution within the subvolume system for various acceptance fractions. These results can be directly mapped to the subvolume (particle) percentage of the total volume (conserved quantities). Our findings are compared to the solenoidal tracker at RHIC (STAR) net-proton and proton data with different energies to investigate the presence of the critical point. Additionally, these results are also compared with the ultrarelativistic quantum molecular dynamics (UrQMD), HRG model, and available lattice data. Published by the American Physical Society 2024

Multivariate copula-based conditional quantiles: analytic higher-order moments and ratio estimation approaches

ABSTRACT In this paper, we aim to modify multivariate copula-based conditional quantiles for a targeted random variable, given multiple random variables attaining their respective quantiles. Specifically, we propose two modifications through the Cornish–Fisher expansion, one of which involves its analytic higher-order unconditional moments. The second one accounts for its higher-order conditional moments estimated using a ratio estimation method. By considering multivariate elliptical and Archimedean copulas with Johnson's SU margins, our simulation study shows that this method provides more accurate conditional moment estimators compared to the naive method. They result in expanded conditional quantile estimators, whose efficiency is relatively better than their unexpanded versions, particularly at lower and higher quantile levels under a stronger (tail) dependence assumption. A much higher efficiency is gained when the first modification is performed. These findings are validated using an empirical study based on cryptocurrency return data and a comparative analysis against the existing estimation approaches.

Information Theoretic Evaluation of Raccoon's Side-Channel Leakage

Raccoon is a lattice-based scheme submitted to the NIST 2022 call for additional post-quantum signatures. One of its main selling points is that its design is intrinsically easy to mask against side-channel attacks. So far, Raccoon's physical security guarantees were only stated in the abstract probing model. In this paper, we discuss how these probing security results translate into guarantees in more realistic leakage models. We also highlight that this translation differs from what is usually observed (e.g., in symmetric cryptography), due to the algebraic structure of Raccoon's operations. For this purpose, we perform an in-depth information theoretic evaluation of Raccoon's most innovative part, namely the AddRepNoise function which allows generating its arithmetic shares on-the-fly. Our results are twofold. First, we show that the resulting shares do not enforce a statistical security order (i.e., the need for the side-channel adversary to estimate higher-order moments of the leakage distribution), as usually expected when masking. Second, we observe that the first-order leakage on the (large) random coefficients manipulated by Raccoon cannot be efficiently turned into leakage on the (smaller) coefficients of its long-term secret. Concretely, our information theoretic evaluations for relevant leakage functions also suggest that Raccoon's masked implementations can ensure high security with less shares than suggested by a conservative analysis in the probing model.

Analysis of the Gaussian assumption of single sound source measured and processed through sound level meter

Machine learning (ML) techniques are constantly growing in acoustics. Such methods exploit large databases to train algorithms and earn complex feature correlations. The primary goal is to obtain inferences and predictions. Thus, ML often exploits statistics, and understanding the data distribution becomes fundamental when analyzing the available data. However, it is well-known that only some common methods can be used with large databases, e.g., normality tests are discouraged. The present work aims to explore the Gaussian assumption underlying a validated clustering technique used in long-term monitoring of sound level meters. The Gaussianity of single sound sources is analyzed through normal tests, normal probability plots, cumulative distribution functions, and high-order moments. The analysis involves a real-world measurement carried out through a sound level meter and speech recordings obtained from a common database used in machine learning. Results show that a single sound source can be deemed Gaussian in sound level meter long-term measurements, leading to important insights concerning the choice of algorithms.

The Lower Limit of Dynamical Black Hole Masses Detectable in Virgo Compact Stellar Systems Using the JWST/NIRSpec IFU

Due to observational challenges, the mass function of black holes (BH) at lower masses is poorly constrained in the local universe. Understanding the occupation fraction of BHs in low-mass galaxies is crucial for constraining the origins of supermassive BH seeds. Compact stellar systems (CSSs), including ultracompact dwarf galaxies (UCDs) and compact elliptical galaxies (cEs), are potential intermediate-mass BH hosts. Despite the difficulties posed by their limited spheres of influence, stellar dynamical modeling has been effective in estimating central BH masses in CSSs. Some CSSs may harbor a BH constituting up to 20% of their host stellar mass, while others might not have a central BH. In support of our ongoing efforts to determine the BH masses in select CSSs in the Virgo cluster using JWST/NIRSpec IFU observations and orbit-superposition dynamical models, we create mock kinematic data mimicking the characteristics of observed cEs/UCDs in the Virgo cluster with different BH masses. We then construct a series of dynamical models using the orbit-superposition code FORSTAND and explore the accuracy of recovering the BH mass. We find that the mass of BHs comprising 1% or more of the total host stellar mass can be accurately determined through kinematic maps featuring higher-order velocity moments. We also assess how BH mass measurement is affected by deprojection methods, regularization factors, anisotropy parameters, orbit initial conditions, the absence of higher-order velocity moments, the spatial resolution, and the signal-to-noise ratio.