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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory

Strong electron correlation plays an important role in transition-metal and heavy-metal chemistry, magnetic molecules, bond breaking, biradicals, excited states, and many functional materials, but it provides a significant challenge for modern electronic structure theory. The treatment of strongly correlated systems usually requires a multireference method to adequately describe spin densities and near-degeneracy correlation. However, quantitative computation of dynamic correlation with multireference wave functions is often difficult or impractical. Multiconfiguration pair-density functional theory (MC-PDFT) provides a way to blend multiconfiguration wave function theory and density functional theory to quantitatively treat both near-degeneracy correlation and dynamic correlation in strongly correlated systems; it is more affordable than multireference perturbation theory, multireference configuration interaction, or multireference coupled cluster theory and more accurate for many properties than Kohn–Sham density functional theory. This perspective article provides a brief introduction to strongly correlated systems and previously reviewed progress on MC-PDFT followed by a discussion of several recent developments and applications of MC-PDFT and related methods, including localized-active-space MC-PDFT, generalized active-space MC-PDFT, density-matrix-renormalization-group MC-PDFT, hybrid MC-PDFT, multistate MC-PDFT, spin–orbit coupling, analytic gradients, and dipole moments. We also review the more recently introduced multiconfiguration nonclassical-energy functional theory (MC-NEFT), which is like MC-PDFT but allows for other ingredients in the nonclassical-energy functional. We discuss two new kinds of MC-NEFT methods, namely multiconfiguration density coherence functional theory and machine-learned functionals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Revealing the nature of electron correlation in transition metal complexes with symmetry breaking and chemical intuition

Here, in this work, we provide a nuanced view of electron correlation in the context of transition metal complexes, reconciling computational characterization via spin and spatial symmetry breaking in single-reference methods with qualitative concepts from ligand-field and molecular orbital theories. These insights provide the tools to reliably diagnose the multi-reference character, and our analysis reveals that while strong (i.e., static) correlation can be found in linear molecules (e.g., diatomics) and weakly bound and antiferromagnetically coupled (monometal-noninnocent ligand or multi-metal) complexes, it is rarely found in the ground-states of mono-transition-metal complexes. This leads to a picture of static correlation that is no more complex for transition metals than it is, e.g., for organic biradicaloids. In contrast, the ability of organometallic species to form more complex interactions, involving both ligand-to-metal σ-donation and metal-to-ligand π-backdonation, places a larger burden on a theory's treatment of dynamic correlation. We hypothesize that chemical bonds in which inter-electron pair correlation is non-negligible cannot be adequately described by theories using MP2 correlation energies and indeed find large errors vs experiment for carbonyl-dissociation energies from double-hybrid density functionals. A theory's description of dynamic correlation (and to a less important extent, delocalization error), which affects relative spin-state energetics and thus spin symmetry breaking, is found to govern the efficacy of its use to diagnose static correlation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Optimal binning of correlated measurements

Experimental measurements are commonly represented on a discrete grid, requiring a balance between granularity and statistical noise. Two strategies have traditionally been used to improve such representations: selecting an appropriate bin width to control discretization error and applying kernel-based smoothing to suppress fluctuations. Despite their shared goal, these approaches have largely developed independently, without a unified statistical description of how discretization and correlation jointly determine measurement precision. Here, we extend the discussion of optimal interval averaging to a correlation-aware setting by Gaussian process regression, which explicitly accounts for correlations among neighboring bins. Starting from first principles, we derive the mean-squared error of discretized measurements and obtain closed-form asymptotic expressions for the optimal bin width and correlation length. When recast in reduced variables, the theory reveals distinct universal scaling laws governing the error in the correlation-free and correlation-controlled regimes. Characterized by intrinsically smooth intensity profiles and counting-based statistics, neutron scattering measurements are well suited for demonstrating the enhanced error contraction enabled by inter-bin correlations. We show that such improvement is achievable over the experimentally accessible Q-range and across multiple instruments and material systems. These results show that explicitly accounting for correlations systematically reshapes the limits of precision in discretized, noise-limited measurements. More broadly, the framework provides a transferable statistical foundation for optimizing data representation, inference, and experimental design across the physical and data sciences.

Tung, Chi-Huan [ORNL] (ORCID:0000000221972074)↗
DOE OSTI2022

Pressure Drop Correlation Improvement for the Near-Wall Region of Pebble-Bed Reactors

Packed beds play an important role in several engineering fields, with their applications in nuclear energy being driven by the development of next-generation reactors utilizing pebble fuel. The random nature of a packed pebble bed creates a flow field that is complex and difficult to predict. Porous media models are an attractive option for modeling pebble-bed reactors (PBRs), as they provide intermediate fidelity results and are computationally efficient. Porous media models, however, rely on the use of correlations to estimate the effect of complicated flow features on the pressure drop and heat transfer in the system. Existing correlations were developed to predict the average behavior of the bed, but they are inaccurate in the near-wall region where the presence of the wall affects the pebble packing. This work aims to investigate the accuracy of a porous media model using the Kerntechnischer Ausschuss (KTA) correlation, the most common pressure drop correlation for PBRs compared to the high-fidelity large eddy simulation (LES). A bed of 1568 pebbles is investigated at Reynolds numbers from 625 to 10 000. The bed is divided into five concentric subdomains to compare the average velocity, friction losses, and form losses between the porous media and LES codes. The comparison between the LES simulation and the KTA correlation revealed that the KTA correlation largely underpredicts the form losses in the near-wall region, leading to an overprediction of the velocity near the wall by nearly 30%. An investigation of the form losses across the range of Reynolds numbers in the LES results provided additional insight into how the KTA correlation may be improved to better predict these spatial effects in a pebble bed. These data suggest that the form coefficient near the wall must be increased by 48% while decreasing the form coefficient of the inner bulk region of the bed by 15%. The implementation of these improvements to the KTA correlation in a porous media model produced a radial velocity profile that saw significantly improved agreement with the LES results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Cosmological cross-correlations and nearest neighbour distributions

ABSTRACT Cross-correlations between data sets are used in many different contexts in cosmological analyses. Recently, k-nearest neighbour cumulative distribution functions (kNN-CDF) were shown to be sensitive probes of cosmological (auto) clustering. In this paper, we extend the framework of NN measurements to describe joint distributions of, and correlations between, two data sets. We describe the measurement of joint kNN-CDFs, and show that these measurements are sensitive to all possible connected N-point functions that can be defined in terms of the two data sets. We describe how the cross-correlations can be isolated by combining measurements of the joint kNN-CDFs and those measured from individual data sets. We demonstrate the application of these measurements in the context of Gaussian density fields, as well as for fully non-linear cosmological data sets. Using a Fisher analysis, we show that measurements of the halo-matter cross-correlations, as measured through NN measurements are more sensitive to the underlying cosmological parameters, compared to traditional two-point cross-correlation measurements over the same range of scales. Finally, we demonstrate how the NN cross-correlations can robustly detect cross-correlations between sparse samples – the same regime where the two-point cross-correlation measurements are dominated by noise.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Dynamical correlations and nonequilibrium sum rules in photodoped Hubbard ladders

Using matrix product state techniques we study the nonequilibrium dynamical response of the half-filled Hubbard ladder when subject to an optical pump. Optical pumping offers a way of producing and manipulating new strongly correlated phenomena by suppressing existing magnetic correlations. The ladder allows the effects of pump directionality to be investigated, and compared to a single chain it has strong spin-charge coupling and a fully gapped excitation spectrum, promising different nonequilibrium physics. We compute time-dependent correlations, including the nonequilibrium dynamical structure factors for spin and charge. By deriving a combined spin-charge sum rule that applies both in and out-of-equilibrium, we show that spectral weight is pumped directly from the antiferromagnetic spin response into a low energy 𝜔 ∼ 0 charge response below the Mott gap. The transfer of weight is pump direction dependent: pumping directed along the legs disrupts magnetic correlations more than pumping in the rung-direction, even if the post-pump energy density is similar. The charge correlation length is dramatically enhanced by the pump, whilst the spin correlations are most strongly suppressed at nearest- and next-nearest-neighbor spacings. After the pump the system is in a nonthermal correlated metallic state, with gapless charge excitations and approximately equal spin and charge correlation lengths, emphasizing the importance of treating these degrees of freedom on an equal footing in nonequilibrium systems.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Neutron-Neutron Correlations in the Photofission of 238U

Background: In the fission of actinides, the nearly back-to-back motion of the fission fragments has a strong effect on the kinematics of fission neutrons. This leads to a favoring of opening angles near 0? and 180? in the neutron-neutron (n-n) opening angle distributions of correlated neutron pairs from the same fission event. Purpose: To measure the n-n opening angle and energy correlations in the photofission of 238U. As of this writing, measurements of correlated n-n opening angle distributions have been reported only for the spontaneous and neutron-induced fission of actinides. This work is the first to report such a measurement using photofission and will provide useful experimental input for photofission models used in codes such as MCNP and FREYA. Method: Fission is induced using bremsstrahlung photons produced via a low duty factor, pulsed, linear electron accelerator. The bremsstrahlung photon beam impinges upon a 238U target that is surrounded by a large neutron scintillation detection system capable of measuring particle position and time of flight, from which n-n opening angle and energy are measured. Neutron-neutron angular correlations are determined by taking the ratio between a correlated neutron distribution and an uncorrelated neutron distribution formed by the pairing of neutrons produced during different beam pulses. This analysis technique greatly diminishes effects due to detector efficiencies, acceptance, and experimental drifts. Results: The angular correlation of neutrons from the photofission of 238U shows a high dependence on neutron energy as well as a dependence on the angle of the emitted neutrons with respect to the incoming photon beam. Angular correlations were also measured using neutrons from the spontaneous fission of 252Cf, showing good agreement with past measurements. Conclusions: The measured angular correlations reflect the underlying back-to-back nature of the fission fragments. An anomalous decline in n-n yield was observed for opening angles near 180? for 238U.

Burggraf, Jeff↗
DOE OSTI2024

Global quark spin correlations in relativistic heavy ion collisions

The observation of the vector meson’s global spin alignment by the STAR Collaboration reveals that strong spin correlations may exist for quarks and antiquarks in relativistic heavy-ion collisions in the normal direction of the reaction plane. We propose a systematic method to describe such correlations in the quark matter. We classify them as local and long range quark spin correlations in the system. We show in particular that the effective quark spin correlations contain the genuine spin correlations originated directly from the dynamical process as well as those induced by averaging over other degrees of freedom. We also show that such correlations can be studied by measuring the vector meson’s spin density matrix and hyperon-hyperon and hyperon-anti-hyperon spin correlations. We present the relationships between these measurable quantities and spin correlations of quarks and antiquarks. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Using Dense Array Waveform Correlations to Build a Velocity Model with Stochastic Variability

In an ongoing effort to improve 3D seismic-wave propagation modeling for frequencies up to 10 Hz, we used cross correlations between vertical-component waveforms from an underground chemical explosion to estimate the statistical properties of small-scale velocity heterogeneities. The waveforms were recorded by a dense 2D seismic array deployed during the Source Physics Experiments for event number 5 (SPE-5) in a series of six underground chemical explosions, conducted at the Nevada National Security Site. The array consisted of 996 geophones with a 50–100 m grid spacing, deployed at the SPE site at the north end of the Yucca Flat basin. The SPE were conducted to investigate the generation and propagation of seismic and acoustic waves from underground explosions. Comparisons of decay rates of waveform cross correlations as function of interstation distance, computed for observed and synthetic seismograms from the SPE-5 chemical explosion, were used to constrain statistical properties of correlated stochastic velocity perturbations representing small-scale heterogeneities added to a geology-based velocity model of the Yucca Flat basin. Using comparisons between recorded and simulated waveform cross correlations, we were able to recover sets of statistical properties of small-scale velocity perturbations in the velocity model that produce the best-fit between the recorded and simulated ground motion. The stochastic velocity fluctuations in the velocity model that produced the smallest misfits have a horizontal correlation distance of between 400 and 800 m, a vertical correlation distance between 100 and 200 m, and a standard deviation of 10% from the nominal model velocity in the alluvium basin layers. They also have a horizontal correlation distance of 1000 m, a vertical correlation distance of 250 m, and a standard deviation of 6% in the underlying and consolidated sedimentary layers, up to a depth of 4 km. Comparisons between observed and simulated wavefields were used to assess the proposed small-scale heterogeneity enhancements to the Yucca Flat basin model. We found that adding a depth-resolved stochastic variability to the geology-based velocity model improves the overall performance of ground-motion simulations of an SPE-5 explosion in the modeled frequency range up to 10 Hz. The results may be applicable to other similar basins.

58 GEOSCIENCES↗
DOE OSTI2024

Physical Correlations and Predictions Emerging from Modern Core-collapse Supernova Theory

Abstract In this paper, we derive correlations between core-collapse supernova observables and progenitor core structures that emerge from our suite of 20 state-of-the-art 3D core-collapse supernova simulations carried to late times. This is the largest such collection of 3D supernova models ever generated and allows one to witness and derive testable patterns that might otherwise be obscured when studying one or a few models in isolation. From this panoramic perspective, we have discovered correlations between explosion energy, neutron star gravitational birth masses, 56 Ni and α -rich freezeout yields, and pulsar kicks and theoretically important correlations with the compactness parameter of progenitor structure. We find a correlation between explosion energy and progenitor mantle binding energy, suggesting that such explosions are self-regulating. We also find a testable correlation between explosion energy and measures of explosion asymmetry, such as the ejecta energy and mass dipoles. While the correlations between two observables are roughly independent of the progenitor zero-age main-sequence (ZAMS) mass, the many correlations we derive with compactness cannot unambiguously be tied to a particular progenitor ZAMS mass. This relationship depends on the compactness/ZAMS mass mapping associated with the massive star progenitor models employed. Therefore, our derived correlations between compactness and observables may be more robust than with ZAMS mass but can nevertheless be used in the future once massive star modeling has converged.

Astronomy & Astrophysics↗
DOE OSTI2021

Uniformly Ordered Binary Decision Algorithm for Benchmark Experiment Correlations in Whisper Validation

When performing a validation exercise for determining the upper subcritical limit of a nuclear criticality safety application, an analyst should select and perform a statistical analysis on a population of benchmark experiments that are neutronically similar to the application. The size of this population should be sufficiently large such that the statistical analysis has a high degree of confidence that the bias plus bias uncertainty (calculational margin) has been accurately quantified. A complication arises because many benchmark experiments share common components, leading to correlations in their measured effective multiplication factors. Correlations between benchmark experiments within the population reduces its predictive power. This motivates the need for methods that consider benchmark experiment correlations and ensure adequate statistical significance of results. The Whisper code is a statistical analysis pack- age that incorporates nuclear data sensitivity coefficients from MCNP to assess benchmark experiment similarity and then performs an extreme-value analysis to estimate the bias plus bias uncertainty. The original methodology in Whisper does not consider the effect of benchmark experiment correlations when making this estimation, and this summary proposes the uniformly ordered binary decision algorithm to address this shortcoming. The original methodology in Whisper computes similarity coefficients ck for an application compared to all benchmark experiments in its library and develops weighting factors for a selected population proportional to the ck values. The methodology can be interpreted as statistically emulating a validation exercise for a particular application where the weighting factors may be viewed as the likelihood that an analyst would include a particular benchmark experiment within the population. The effective sample size of the population is the expected or mean number of benchmark experiments in the population. The uniformly ordered binary decision algorithm identifies clusters of correlated benchmark experiments within the population and then computes adjusted weighting factors based on the magnitude of the correlation coefficients within the cluster to compute a reduced effective sample size accounting for the lower information content because of correlations. Benchmark experiments within the cluster are ordered randomly with equal probability and probabilistic decisions are made as to whether a benchmark. experiment within the cluster should treated as redundant with a previous one; if two redundant benchmark experiments are included, then the conservative worst case bias plus bias uncertainty is used and the pair is counted as a single benchmark experiment in the population. Results are provided for HEU solutions in a research version of the Whisper software using benchmark experiment correlations provided by DICE, the Database for the International Criticality Safety Benchmark Evaluation Project (ICSBEP). These show that there can be a significant increase in the bias plus bias uncertainty because the effective sample size is reduced, and therefore the algorithm, needing to meet sample size requirements, expands the benchmark experiment population by accepting less similar benchmark experiments that would have otherwise not been included.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Correlation Calculations for the Russian Pu Metal Fast Experiments

Nuclear criticality experiments are often conducted in campaigns with multiple variations. These experiments reuse the same basic components, like the fuel, moderator, or positioning machines. The components have uncertainties in their geometry and composition that propagate to models of the experiments. Shared components create shared uncertainty between the $k_{eff}$ of benchmarks. The shared uncertainty is commonly quantified with a covariance, or correlation coefficient. These covariances can impact criticality safety and nuclear data validation applications. While benchmark evaluations tabulate an experiment’s uncertainty, they often lack a detailed calculation of correlations between experiments. Even some very commonly used benchmarks, like the Russian Pu Metal Fast (PMF) experiments, have missing correlations. This paper presents our approach to calculate the correlations for five of the Russian PMF experiments. The experiments share hemispherical Pu shells that induce a correlation between modeled $k_{eff}$ values. We estimated the correlations with simplified and detailed models of the experiments through linear-perturbation theory. The correlations between the experiments vary significantly between the detailed vs. simplified models. We also investigate how the correlations affect validation metrics of the experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Bandwidth Control and Symmetry Breaking in a Mott‐Hubbard Correlated Metal

Abstract In Mott materials strong electron correlation yields a spectrum of complex electronic structures. Recent synthesis advancements open realistic opportunities for harnessing Mott physics to design transformative devices. However, a major bottleneck in realizing such devices remains the lack of control over the electron correlation strength. This stems from the complexity of the electronic structure, which often veils the basic mechanisms underlying the correlation strength. This study presents control of the correlation strength by tuning the degree of orbital overlap using picometer‐scale lattice engineering. This study illustrates how bandwidth control and concurrent symmetry breaking can govern the electronic structure of a correlated SrVO 3 model system. This study shows how tensile and compressive biaxial strain oppositely affect the SrVO 3 in‐plane and out‐of‐plane orbital occupancy, resulting in the partial alleviation of the orbital degeneracy. The spectral weight redistribution under strain is derived and explained, which illustrates how high tensile strain drives the system toward a Mott insulating state. Implementation of such concepts can push correlated electron phenomena closer toward new solid‐state devices and circuits. These findings therefore pave the way for understanding and controlling electron correlation in a broad range of functional materials, driving this powerful resource for novel electronics closer toward practical realization.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Measurement of D 0 -meson + hadron two-dimensional angular correlations in Au + Au collisions at s N N = 200 GeV

Open heavy flavor hadrons provide unique probes of the medium produced in ultra-relativistic heavy-ion collisions. Due to their increased mass relative to light-flavor hadrons, long lifetime, and early production in hard-scattering interactions, they provide access to the full evolution of the partonic medium formed in heavy-ion collisions. This paper reports two-dimensional (2D) angular correlations between neutral D-mesons and unidentified charged particles produced in minimum-bias Au+Au collisions at s N N = 200 GeV. D 0 and D 0 ¯ mesons are reconstructed via their weak decay to K ∓ π ± using the Heavy Flavor Tracker (HFT) in the Solenoidal Tracker at RHIC (STAR) experiment. Correlations on relative pseudorapidity and azimuth (Δη,ΔΦ) are presented for peripheral, mid-central and central collisions with D 0 transverse momentum from 2 to 10 GeV/c. Attention is focused on the 2D peaked correlation structure near the triggered D 0 -meson, the {\em near-side} (NS) peak, which serves as a proxy for a charm-quark containing jet. The correlated NS yield of charged particles per D 0 -meson and the 2D widths of the NS peak increase significantly from peripheral to central collisions. These results are compared with similar correlations using unidentified charged particles, consisting primarily of light-flavor hadrons, at similar trigger particle momenta. Similar per-trigger yields and widths of the NS correlation peak are observed. Here, the present results provide additional evidence that D 0 -mesons undergo significant interactions with the medium formed in heavy-ion collision and show, for the first time, significant centrality evolution of the NS 2D peak in the correlations of particles associated with a heavy-flavor hadron produced in these collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Variation of carrier density in semimetals via short-range correlation: A case study with nickelate NdNiO 2

Carrier density is one of the key controlling factors of material properties, particularly in controlling the essential correlations in strongly correlated materials. Typically, carrier density is externally tuned by doping or gating and remains fixed below room temperature. Strangely, the carrier density in correlated semimetals is often found to vary sensitively against weak external controls such as temperature, magnetic field, and pressure. Here, we develop a realistic simulation scheme that incorporates interatomic noncollinear magnetic correlation without a long-range order. Using the recently discovered nickelate superconductor as an example, we demonstrate a rather generic low-energy mechanism that in semimetals short-range correlation can reversely modulate the carrier density as well. Such a mutual influence between correlation and carrier density provides an extra ingredient for sensitive bifurcating behavior. This special feature of correlated semimetals explains their versatile carrier density at low energy and opens up new possibilities of functionalizing these materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Differential two-particle number and momentum correlations with the AMPT, UrQMD, and EPOS models in Pb-Pb collisions at s N N = 2.76 TeV

We report studies of charge-independent and charge-dependent two-particle differential number correlation functions, R 2 (Δη,Δφ), and transverse momentum correlation functions, P 2 (Δη,Δφ), of charged particles produced in Pb–Pb collisions at the LHC center-of-mass energy √sNN= 2.76 TeV with the UrQMD, AMPT, and EPOS models. Model calculations for R2 and P2 correlation functions are presented for inclusive charged hadrons (h ± ) in selected transverse momentum ranges and with full azimuthal coverage in the pseudorapidity range |η|<1.0. We compare these calculations for the strength, shape, and particularly the width of the correlation functions with recent measurements of these observables by the ALICE collaboration. Our analysis indicates that comparative studies of R 2 and P 2 correlation functions provide valuable insight towards the understanding of particle production in Pb–Pb collisions. We find, in particular, that these models produce quantitatively different magnitudes and shapes for these correlation functions and none reproduce the results reported by the ALICE collaboration. Accounting for quantum number conservation in models, particularly charge conservation, is mandatory to reproduce the detailed measurements of number and transverse momentum correlation functions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Measurement of the Sensitivity of Two-Particle Correlations in $\mathcal{pp}$ Collisions to the Presence of Hard Scatterings

A key open question in the study of multiparticle production in high-energy pp collisions is the relationship between the “ridge”—i.e., the observed azimuthal correlations between particles in the underlying event that extend over all rapidities—and hard or semihard scattering processes. In particular, it is not known whether jets or their soft fragments are correlated with particles in the underlying event. To address this question, two-particle correlations are measured in pp collisions at $\sqrt{s}$=13 TeV using data collected by the ATLAS experiment at the LHC, with an integrated luminosity of 15.8 pb -1 , in two different configurations. In the first case, charged particles associated with jets are excluded from the correlation analysis, while in the second case, correlations are measured between particles within jets and charged particles from the underlying event. Second-order flow coefficients, v2, are presented as a function of event multiplicity and transverse momentum. These measurements show that excluding particles associated with jets does not affect the measured correlations. Moreover, particles associated with jets do not exhibit any significant azimuthal correlations with the underlying event, ruling out hard processes contributing to the ridge.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Inference for Nonparanormal Partial Correlation via Regularized Rank-Based Nodewise Regression

Abstract Partial correlation is a common tool in studying conditional dependence for Gaussian distributed data. However, partial correlation being zero may not be equivalent to conditional independence under non-Gaussian distributions. In this paper, we propose a statistical inference procedure for partial correlations under the high-dimensional nonparanormal (NPN) model where the observed data are normally distributed after certain monotone transformations. The NPN partial correlation is the partial correlation of the normal transformed data under the NPN model, which is a more general measure of conditional dependence. We estimate the NPN partial correlations by regularized nodewise regression based on the empirical ranks of the original data. A multiple testing procedure is proposed to identify the nonzero NPN partial correlations. The proposed method can be carried out by a simple coordinate descent algorithm for lasso optimization. It is easy-to-implement and computationally more efficient compared to the existing methods for estimating NPN graphical models. Theoretical results are developed to show the asymptotic normality of the proposed estimator and to justify the proposed multiple testing procedure. Numerical simulations and a case study on brain imaging data demonstrate the utility of the proposed procedure and evaluate its performance compared to the existing methods. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.

97 MATHEMATICS AND COMPUTING↗