Article
Biology
Ghulam A. Qadir, Ying Sun
Summary: The paper proposes a semiparametric approach for estimating multivariate spatial covariance function, using spectral representations for approximate Matern marginals and highly flexible cross-covariance functions. The flexibility in cross-covariance function is achieved through specifying underlying coherence functions with B-splines, allowing capture of nontrivial cross-spectral features.
Article
Biology
Debangan Dey, Abhirup Datta, Sudipto Banerjee
Summary: For multivariate spatial Gaussian process models, traditional specifications of cross-covariance functions do not effectively utilize relational inter-variable graphs to ensure process-level conditional independence between the variables. We propose a new method that uses stitching to construct cross-covariance functions from graphs, ensuring process-level conditional independence between variables.
Article
Computer Science, Interdisciplinary Applications
Jonathan Acosta, Alfredo Alegria, Felipe Osorio, Ronny Vallejos
Summary: This article discusses the definition and evaluation of effective sample size (ESS), proposing an alternative definition based on Godambe information and investigating the theoretical properties satisfied by this quantity. The authors evaluate their proposal in several parametric correlation structures, with simulation experiments showing accurate approximations of full likelihood-based ESS while maintaining a moderate computational cost. The proposed framework is analyzed on a large dataset to quantify its effectiveness and limitations in practice.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2021)
Article
Statistics & Probability
Cheng Li, Saifei Sun, Yichen Zhu
Summary: This article investigates the estimation of finite-dimensional covariance parameters in spatial Gaussian process regression models. We propose a Bayesian estimation approach under fixed-domain asymptotics and a novel adaptation of Schwartz's consistency theorem for showing posterior contraction rates of the covariance parameters. We derive a new polynomial evidence lower bound and propose consistent higher-order quadratic variation estimators. Our theory provides explicit posterior contraction rates for the microergodic and nugget parameters in the isotropic Matern covariance function under a general stratified sampling design. Simulation studies and an application to sea surface temperature data validate our theory and Bayesian predictive performance.
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
(2023)
Article
Computer Science, Interdisciplinary Applications
Rui Meng, Braden Soper, Herbert K. H. Lee, Vincent X. Liu, John D. Greene, Priyadip Ray
Summary: This study introduces a novel nonstationary multivariate Gaussian process model for EHR data which can capture time-varying scale, correlation, and smoothness across multiple clinical variables. The model is validated using Maximum a posteriori and Hamilton Monte Carlo inference methods, demonstrating effectiveness on actual EHR data. Additionally, statistically significant correlations between a clinical patient risk metric and the latent processes of the proposed model are investigated using EHR data from Kaiser Permanente Division of Research.
JOURNAL OF BIOMEDICAL INFORMATICS
(2021)
Article
Geochemistry & Geophysics
Gael Kermarrec, Michael Loesler
Summary: In this study, the impact of an enhanced stochastic model on biases is examined, and a diagonal correlation model (DCM) is proposed to account for correlations. The benefits and improvements of using this new model are evaluated against the traditional methods.
JOURNAL OF GEODESY
(2021)
Article
Geosciences, Multidisciplinary
Denis Allard, Lucia Clarotto, Xavier Emery
Summary: This paper extends the well-known class of space-time covariance functions, Gneiting class, by introducing a highly flexible parametric class of fully nonseparable direct and cross-covariance functions for multivariate random fields. The proposed model allows each component to have its own spatial covariance function and correlation function in time, offering more complexity and flexibility compared to existing models. The paper provides sufficient conditions for valid models and discusses the parameterization. Simulation algorithms for continuous-in-space and discrete-in-time settings are also presented.
SPATIAL STATISTICS
(2022)
Article
Environmental Sciences
Guofeng Wang, Qinyang Guo, Xinsheng Zhou, Fan Zhang
Summary: This study constructs a multi-region input-output database using the Eora database and analyzes the spatial correlation network of embodied net carbon transfer in global agricultural trade. The results show that the network is densely connected and has significant spatial correlation spillover effects.
ENVIRONMENTAL SCIENCE AND POLLUTION RESEARCH
(2023)
Article
Geosciences, Multidisciplinary
Michael L. L. Stein
Summary: The estimation of range parameters for spatial covariance functions is a challenging problem in spatial statistics. This study explores the possibility of extending the domain of the inverse range parameter to negative values in certain situations, as long as the spatial domain of interest is bounded. Numerical work, limited theory, and an application to elevation data are used to provide further insight into this phenomenon and the difficulties in estimating range parameters.
SPATIAL STATISTICS
(2022)
Article
Engineering, Environmental
Angelica Maria Tortola Ribeiro, Paulo Justiniano Ribeiro Junior, Wagner Hugo Bonat
Summary: This paper proposes a covariance specification for modeling spatially continuous multivariate data. The model is based on a reformulation of Kronecker's product of covariance matrices for Gaussian random fields and is applicable to different covariance functions. Compared to classical models, this model has the advantages of a simple structure, reduced estimation time, and flexible generalization.
STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT
(2022)
Article
Geosciences, Multidisciplinary
A. Alegria, F. Cuevas-Pacheco, P. Diggle, E. Porcu
Summary: The Matern family of isotropic covariance functions plays a central role in the development and application of statistical models for geospatial data, but has limitations when modeling data on the sphere. This paper proposes a new family of isotropic covariance functions for random fields defined over the sphere, with a parameter to index the mean square differentiability and allow for a range of fractal dimensions.
SPATIAL STATISTICS
(2021)
Article
Statistics & Probability
Mitchell L. Krock, William Kleiber, Dorit Hammerling, Stephen Becker
Summary: We propose a new modeling framework that combines ideas from multiscale and spectral approaches with graphical models for highly multivariate spatial processes. We extend the basis graphical lasso to a multivariate Gaussian process, where the basis functions are weighted with Gaussian graphical vectors. Our model assumes that the basis functions represent different levels of resolution and the graphical vectors for each level are independent. The use of orthogonal basis functions reduces computational complexity and memory usage. An additional fusion penalty promotes a parsimonious conditional independence structure in the multilevel graphical model. We demonstrate our method on a large climate ensemble from the National Center for Atmospheric Research's Community Atmosphere Model.
JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
(2023)
Article
Biology
Sze Him Leung, Ji Meng Loh, Chun Yip Yau, Zhengyuan Zhu
Summary: This paper introduces a new spatial sampling design procedure based on the GNS process. By optimizing the parameter sets in this process, sampling points can be selected more efficiently, making the proposed algorithm applicable to larger sample sizes while achieving similar minimization of criterion functions compared to traditional methods.
JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS
(2021)
Article
Astronomy & Astrophysics
Marc Tunnell, Nathaniel Bowman, Erin Carrier
Summary: The NASA Ames Mars Global Climate Model (MGCM) is a computer model that simulates the weather on Mars. The MGCM is used by NASA to help understand weather data collected from satellites and other sources. To address the computational challenge of sensitivity studies, a surrogate model using Gaussian processes (GP) has been developed. This surrogate model can accurately and quickly approximate the output of the MGCM with a relatively small amount of training data.
EARTH AND SPACE SCIENCE
(2023)
Article
Engineering, Electrical & Electronic
Zbynek Koldovsky, Vaclav Kautsky, Petr Tichavsky
Summary: This article introduces new algorithms for ICE/IVE by combining nonstationary mixing and source models, allowing for a moving source-of-interest distribution. The proposed Gaussian source model shows benefits in frequency-domain speaker extraction. The algorithms are verified in simulations and demonstrate superior performance in convergence speed and extraction accuracy compared to existing algorithms.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2022)
Article
Statistics & Probability
Tsung- Lin, Wan-Lun Wang
Summary: This paper derives explicit expressions for the moments of truncated multivariate normal/independent distributions with supports confined within a hyper-rectangle. A Monte Carlo experiment is conducted to validate the proposed formulae for five selected members of the distributions.
JOURNAL OF MULTIVARIATE ANALYSIS
(2024)
Article
Statistics & Probability
Tao Qiu, Qintong Zhang, Yuanyuan Fang, Wangli Xu
Summary: This article introduces a method for testing the homogeneity of two random vectors. The method involves selecting two subspaces and projecting them onto one-dimensional spaces, using the Cramer-von Mises distance to construct the test statistic. The performance is enhanced by repeating this procedure and the effectiveness is demonstrated through numerical simulations.
JOURNAL OF MULTIVARIATE ANALYSIS
(2024)
Article
Statistics & Probability
Alfredo Alegria, Xavier Emery
Summary: This study contributes to covariance modeling by proposing new parametric families of isotropic matrix-valued functions that exhibit non-monotonic behaviors, such as hole effects and cross-dimples. The benefit of these models is demonstrated on a bivariate dataset of airborne particulate matter concentrations.
JOURNAL OF MULTIVARIATE ANALYSIS
(2024)
Article
Statistics & Probability
Kento Egashira, Kazuyoshi Yata, Makoto Aoshima
Summary: This study investigates the asymptotic properties of hierarchical clustering in different settings, including high-dimensional, low-sample-size scenarios. The results show that hierarchical clustering exhibits good asymptotic properties under practical settings for high-dimensional data. The study also extends the analysis to consider scenarios where both the dimension and sample size approach infinity, and generalizes the concept of populations in multiclass HDLSS settings.
JOURNAL OF MULTIVARIATE ANALYSIS
(2024)
Article
Statistics & Probability
Marlene Baumeister, Marc Ditzhaus, Markus Pauly
Summary: This paper introduces a more robust multivariate analysis method by using general quantiles, particularly the median, instead of the traditional mean, and applies and validates this method on various factorial designs. The effectiveness of this method is demonstrated through theoretical and simulation studies on small and moderate sample sizes.
JOURNAL OF MULTIVARIATE ANALYSIS
(2024)
Article
Statistics & Probability
Chuancun Yin, Narayanaswamy Balakrishnan
Summary: The family of multivariate skew-normal distributions has interesting properties, which also hold for a general class of skew-elliptical distributions.
JOURNAL OF MULTIVARIATE ANALYSIS
(2024)
Article
Statistics & Probability
Gaspard Bernard, Thomas Verdebout
Summary: In this paper, we address the problem of testing the relationship between the eigenvalues of a scatter matrix in an elliptical distribution. Using the Le Cam asymptotic theory, we show that the non-specification of nuisance parameters has an asymptotic cost for testing the relationship. We also propose a distribution-free signed-rank test for this problem.
JOURNAL OF MULTIVARIATE ANALYSIS
(2024)