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multivariate spatial data visualization: a survey

JOURNAL OF VISUALIZATION 2019年第5期22卷 897-912页

作者： He, Xiangyang Tao, Yubo Wang, Qirui Lin, Hai Zhejiang Univ State Key Lab CAD & CG Hangzhou Zhejiang Peoples R China

multivariate spatial data play an important role in computational science and engineering simulations. The potential features and hidden relationships in multivariate data can assist scientists to gain an in-depth understanding of a scientific process, verify a hypothesis, and further discover a new physical or chemical law. In this paper, we present a comprehensive survey of the state-of-the-art techniques for multivariate spatial data visualization. We first introduce the basic concept and characteristics of multivariate spatial data, and describe three main tasks in multivariate data visualization: feature classification, fusion visualization, and correlation analysis. Finally, we prospect potential research topics for multivariate data visualization according to the current research.

关键词： multivariate spatial data Feature classification Fusion visualization Correlation analysis

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Inference for Complex Computer Models and Large multivariate spatial data with Applications to Climate Science

Inference for Complex Computer Models and Large Multivariate...

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作者： Bhat, Kabekode PennState University Libraries

学位级别：Doctor of Philosophy

Computer model calibration involves combining information from simulations of a complex computer model with observations of the process being simulated by the model. Increasingly, computer model output is in the form of multiple spatial fields, particularly in climate science. We develop several new approaches for computer model calibration for multivariate spatial data. We first describe an inferential approach using Gaussian processes to emulate the computer model, thereby establishing a connection between the calibration parameters and the multiple spatial fields. We carry out statistical inference for the climate parameters using a Bayesian approach, accounting for spatial dependence, model discrepancy and other sources of uncertainty. We conduct a study of the merits of including a model discrepancy term in the statistical model. One flexible model we develop allows for non-linear relationships among the spatial fields by modeling the spatial fields using a conditional hierarchical approach. Further, we develop a new flexible computationally tractable approach for calibration combining three or more multiple spatial fields using a Linear Model of Coregionalization (LMC) allowing for a non-separable covariance, reducing data-specific modeling decisions, and for a more flexible construction of model discrepancy. We demonstrate an application of our approach to infer vertical diffusivity, a climate parameter that plays a key role in obtaining probabilistic projections of the Atlantic Meridional Overturning Circulation (MOC). As changes in the MOC may result in major disruptions to the climate, MOC projections are of great interest to climate scientists and policy makers. We utilize kernel mixing and matrix identities in our Gaussian process model in order to make computations tractable for large spatial data sets. In addition, we may have hindcasts and historical data from multiple computer climate models. We introduce and apply an new approach using Bayesian Mode

关键词： computer experiments Gaussian process multivariate spatial data spatiotemporal data hierarchical Bayesian modeling climate change

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Optimal network design for Bayesian spatial prediction of multivariate non-Gaussian environmental data

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JOURNAL OF APPLIED STATISTICS 2016年第7期43卷 1335-1348页

作者： Rivaz, Firoozeh Shahid Beheshti Univ Fac Math Sci Dept Stat Tehran Iran

This paper deals with the problem of increasing air pollution monitoring stations in Tehran city for efficient spatial prediction. As the data are multivariate and skewed, we introduce two multivariate skew models through developing the univariate skew Gaussian random field proposed by Zareifard and Jafari Khaledi [21]. These models provide extensions of the linear model of coregionalization for non-Gaussian data. In the Bayesian framework, the optimal network design is found based on the maximum entropy criterion. A Markov chain Monte Carlo algorithm is developed to implement posterior inference. Finally, the applicability of two proposed models is demonstrated by analyzing an air pollution data set.

关键词： air pollution Bayesian sampling design entropy linear model of coregionalization multivariate spatial data skew Gaussian process

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multivariate spatial modelling through a convolution-based skewed process

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STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT 2019年第3期33卷 657-671页

作者： Zareifard, Hamid Khaledi, Majid Jafari Dahdouh, Omar Jahrom Univ Dept Stat Jahrom *** Iran Tarbiat Modares Univ Dept Stat POB 14115-134 Tehran Iran

In some statistical issues, several continuous spatial outcomes are simultaneously measured at each sampling location. In such circumstances, it is common to model the data through a multivariate Gaussian model. As the normality assumption is often untenable, this paper proposes a multivariate skewed spatial model which, by virtue of its capacity for capturing skewness, is potentially more flexible than symmetric ones. Specifically, a multivariate version of the Gaussian-log Gaussian convolution process is developed. The resulting covariance for the multivariate process is in general nonseparable. We also discuss the other properties of the induced covariance function. Furthermore, Markov chain Monte Carlo methods are used to make Bayesian inferences. The performance of the method is investigated through simulation experiments and by analyzing a real soil pollution dataset obtained from Golestan province, North of Iran.

关键词： multivariate spatial data Non-Gaussian modelling Bayesian analysis Convolution Cross-dependency structure

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A Kronecker-based covariance specification for spatially continuous multivariate data

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STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT 2022年第12期36卷 4087-4102页

作者： Tortola Ribeiro, Angelica Maria Ribeiro Junior, Paulo Justiniano Bonat, Wagner Hugo Fed Technol Univ Parana Acad Dept Stat BR-80230901 Curitiba Parana Brazil Univ Fed Parana Dept Stat BR-81530000 Curitiba Parana Brazil Univ Fed Parana Postgrad Program Numer Methods Engn BR-81530000 Curitiba Parana Brazil

We propose a covariance specification for modeling spatially continuous multivariate data. This model is based on a reformulation of Kronecker's product of covariance matrices for Gaussian random fields. The structure holds for different choices of covariance functions with parameters varying in their usual domains. In comparison with classical models from the literature, we used the Matern correlation function to specify the marginal covariances. We also assess the reparametrized generalized Wendland model as an option for efficient calculation of the Cholesky decomposition, improving the model's ability to deal with large data sets. The reduced computational time and flexible generalization for increasing number of variables, make it an attractive alternative for modelling spatially continuous data. The proposed model is fitted to a soil chemistry properties dataset, and adequacy measures, forecast errors and estimation times are compared with the ones obtained based on classical models. In addition, the model is fitted to a North African temperature dataset to illustrate the model's flexibility in dealing with large data. A simulation study is performed considering different parametric scenarios to evaluate the properties of the maximum likelihood estimators. The simple structure and reduced estimation time make the proposed model a candidate approach for multivariate analysis of spatial data.

关键词： Gaussian random fields Covariance functions Geostatistics Matern correlation model multivariate spatial data

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multivariate Spartan spatial random field models

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PROBABILISTIC ENGINEERING MECHANICS 2014年第0期37卷 84-92页

作者： Hristopulos, Dionissios T. Porcu, Emilio Tech Univ Crete Dept Mineral Resources Engn Geostat Res Unit Khania 73100 Greece Univ Tecn Federico Santa Maria Dept Math Valparaiso Chile

This paper introduces a family of stationary multivariate spatial random fields with D scalar components that extend the scalar model of Gibbs random fields with local interactions (i.e., Spartan spatial random fields). We derive permissibility conditions for Spartan multivariate spatial random fields with a specific structure of local interactions. We also present explicit expressions for the respective matrix covariance functions obtained at the limit of infinite spectral cutoff in one, two and three spatial dimensions. Finally, we illustrate the proposed covariance models by means of simulated bivariate time series and two-dimensional random fields. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Cramer's theorem Stationary multivariate spatial data multivariate time series Simulation

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Semiparametric estimation of cross-covariance functions for multivariate random fields

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BIOMETRICS 2021年第2期77卷 547-560页

作者： Qadir, Ghulam A. Sun, Ying King Abdullah Univ Sci & Technol KAUST Comp Elect & Math Sci & Engn Div CEMSE Thuwal 239556900 Saudi Arabia

The prevalence of spatially referenced multivariate data has impelled researchers to develop procedures for joint modeling of multiple spatial processes. This ordinarily involves modeling marginal and cross-process dependence for any arbitrary pair of locations using a multivariate spatial covariance function. However, building a flexible multivariate spatial covariance function that is nonnegative definite is challenging. Here, we propose a semiparametric approach for multivariate spatial covariance function estimation with approximate Matern marginals and highly flexible cross-covariance functions via their spectral representations. The flexibility in our cross-covariance function arises due to B-spline-based specification of the underlying coherence functions, which in turn allows us to capture nontrivial cross-spectral features. We then develop a likelihood-based estimation procedure and perform multiple simulation studies to demonstrate the performance of our method, especially on the coherence function estimation. Finally, we analyze particulate matter concentrations (PM2.5) and wind speed data over the West-North-Central climatic region of the United States, where we illustrate that our proposed method outperforms the commonly used full bivariate Matern model and the linear model of coregionalization for spatial prediction.

关键词： coherence function co-kriging matern covariance multivariate spatial data

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Synthetic scenario generation of monthly streamflows conditioned to the El Nino-Southern Oscillation: application to operation planning of hydrothermal systems

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STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT 2020年第2期34卷 331-353页

作者： Treistman, Felipe Pineiro Maceira, Maria Elvira Jardim Penna, Debora Dias Damazio, Jorge Machado Rotunno Filho, Otto Correa Elect Energy Res Ctr Cepel Horacio Macedo Ave 354Cidade Univ BR-21941911 Rio De Janeiro RJ Brazil Fed Univ Rio de Janeiro UFRJ Alberto Luiz Coimbra Inst Postgrad Studies & Res Civil Engn Program Horacio Macedo Ave 2020Cidade Univ BR-21941914 Rio De Janeiro RJ Brazil State Univ Rio de Janeiro UERJ Rio De Janeiro Brazil

The Brazilian Interconnected Power System is hydro dominated and characterized by large reservoirs presenting multi-year regulation capability, arranged in complex cascades over several river basins. In this way, the expansion and operation planning should take into account the uncertainties about the future inflows to hydroplants reservoirs. Currently, a stochastic model for synthetic scenarios generation of monthly streamflow, based on Periodic Auto-Regressive formulation, is used to address the uncertainty. This is the official model used in the Brazilian energy operation planning by the Ministry of Mines and Energy, the National Operator of Electrical System, the Chamber of Electric Energy Commercialization and the Energy Planning Company. Recently, a great scientific effort has been made to include relevant climatic information in stochastic streamflow models. Among several important climatic phenomena in the Brazilian hydrological cycles, El Nino-Southern Oscillation has been pointed as one of the most important. Although the stochastic models that include exogenous variables or that use wavelets present good results, they have limitations for long-term horizon projections or are not suitable for applications that use stochastic dual dynamic programming, which is the case of the Brazilian electrical system. This work proposes an improvement to the current scenario generation model, in order to consider the climate information, but still being suitable to be applied in SDDP algorithms. To achieve this goal, a Markov-Switching Periodic Auto-Regressive model is presented. It is demonstrated that the methodology is able to generate synthetic scenarios which better resembles the observed streamflow, mainly during periods when the streamflow are below-average.

关键词： Synthetic streamflow scenario generation multivariate spatial data El Nino-Southern Oscillation Energy operation planning

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Linking ArcView™ and XGobi:: Insight behind the front end

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2000年第3期9卷 470-490页

作者： Symanzik, J Cook, D Lewin-Koh, N Majure, JJ Megretskaia, I Utah State Univ Dept Math & Stat Logan UT 84322 USA Iowa State Univ Dept Stat Ames IA 50011 USA Harvard Univ Cambridge MA 02138 USA

This article presents aspects of the implementation of a bidirectional link between the Geographic Information System (GIS) ArcView(TM) and the interactive dynamic statistical graphics program XGobi. We describe the main functionality of the link, the underlying remote procedure call (RPC) mechanism, and internal data structures, and discuss topics such as security, concurrency, and linked brushing. We think that these topics are of particular interest to software authors intending to link similar software packages, and software users learning about strengths (and weaknesses) of the implementation of our link.

关键词： cartographic data dynamic statistical graphics Geographic information system interprocess communication multivariate spatial data spatial cumulative distribution function spatially lagged scatterplot spatial statistics variogram-cloud plot

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Analysis of contaminant co-occurrence in community water systems

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2004年第465期99卷 45-56页

作者： Lockwood, JR Schervish, MJ Gurian, PL Small, MJ RAND Corp Stat Grp Pittsburgh PA 15213 USA Univ Texas Dept Civil Engn El Paso TX 79968 USA Carnegie Mellon Univ Dept Engn & Publ Policy Pittsburgh PA 15213 USA Carnegie Mellon Univ Dept Civil & Environm Engn Pittsburgh PA 15213 USA Carnegie Mellon Univ Dept Stat Pittsburgh PA 15213 USA

The current framework for U.S. Environmental Protection Agency regulation of water quality in community drinking water supplies produces sequential rules for either single contaminants or small groups of similar contaminants. For both substantive and pragmatic reasons, some water industry experts have advocated the development of a more holistic regulatory process in which rules are promulgated less frequently but for larger contaminant classes. Such a framework would require the expansion of existing regulatory evaluation technologies to account for joint occurrence distributions of multiple contaminants. This article presents an analysis, using two national contaminant databases, of the joint distributions of seven contaminants (arsenic, nitrate, uranium, manganese, magnesium, calcium, and sulfate) in community water system source waters. Inferences are based on a flexible Bayesian hierarchical modeling structure with numerous features desirable for empirical exploration of multicontaminant regulations, including the simultaneous estimation of spatial heterogeneity in contaminant levels and covariations among contaminants, applicability to sparse data collected over a large spatial scale, and coherent assimilation of information provided by censored observations. The model is used to estimate a family of joint distributions for the contaminants indexed by water system characteristics, with empirically appropriate complexity given the resolution of the available data. The resulting distributions provide insights about the nature of, and uncertainty about, contaminant co-occurrence patterns, quantify the impact on national assessments of jointly modeling the contaminants, and facilitate identification of critical classes of water systems where uncertainty is highest.

关键词： data augmentation Markov chain Monte carlo multivariate spatial data regulatory impact assessment water quality regulation

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