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Reduced Dimension Hierarchical Statistical Models For Spatial And Spatio Temporal Data
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Book Synopsis Reduced-dimension Hierarchical Statistical Models for Spatial and Spatio-temporal Data by : Lei Kang
Download or read book Reduced-dimension Hierarchical Statistical Models for Spatial and Spatio-temporal Data written by Lei Kang and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Moreover, we extend the SRE model to the Spatio-Temporal Random Effects (STRE) model for massive spatio-temporal datasets. We explicitly model the measurement error, the non-dynamic fine-scale variation, the dynamic spatial variation, and the trend. The optimal spatio-temporal predictions are derived efficiently through the fixed-rank model and a rapid recursive updating procedure through the Kalman filter. Formulas for optimal smoothing, filtering, and forecasting are derived. The improvement of combining past and current data using the methodology called Fixed Rank Filtering (FRF) to predict the current hidden process of interest, is illustrated with a simulation experiment. The methodology is also applied to a large spatio-temporal remote-sensing dataset.
Book Synopsis Statistics for Spatio-Temporal Data by : Noel Cressie
Download or read book Statistics for Spatio-Temporal Data written by Noel Cressie and published by John Wiley & Sons. This book was released on 2015-11-02 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: Winner of the 2013 DeGroot Prize. A state-of-the-art presentation of spatio-temporal processes, bridging classic ideas with modern hierarchical statistical modeling concepts and the latest computational methods Noel Cressie and Christopher K. Wikle, are also winners of the 2011 PROSE Award in the Mathematics category, for the book “Statistics for Spatio-Temporal Data” (2011), published by John Wiley and Sons. (The PROSE awards, for Professional and Scholarly Excellence, are given by the Association of American Publishers, the national trade association of the US book publishing industry.) Statistics for Spatio-Temporal Data has now been reprinted with small corrections to the text and the bibliography. The overall content and pagination of the new printing remains the same; the difference comes in the form of corrections to typographical errors, editing of incomplete and missing references, and some updated spatio-temporal interpretations. From understanding environmental processes and climate trends to developing new technologies for mapping public-health data and the spread of invasive-species, there is a high demand for statistical analyses of data that take spatial, temporal, and spatio-temporal information into account. Statistics for Spatio-Temporal Data presents a systematic approach to key quantitative techniques that incorporate the latest advances in statistical computing as well as hierarchical, particularly Bayesian, statistical modeling, with an emphasis on dynamical spatio-temporal models. Cressie and Wikle supply a unique presentation that incorporates ideas from the areas of time series and spatial statistics as well as stochastic processes. Beginning with separate treatments of temporal data and spatial data, the book combines these concepts to discuss spatio-temporal statistical methods for understanding complex processes. Topics of coverage include: Exploratory methods for spatio-temporal data, including visualization, spectral analysis, empirical orthogonal function analysis, and LISAs Spatio-temporal covariance functions, spatio-temporal kriging, and time series of spatial processes Development of hierarchical dynamical spatio-temporal models (DSTMs), with discussion of linear and nonlinear DSTMs and computational algorithms for their implementation Quantifying and exploring spatio-temporal variability in scientific applications, including case studies based on real-world environmental data Throughout the book, interesting applications demonstrate the relevance of the presented concepts. Vivid, full-color graphics emphasize the visual nature of the topic, and a related FTP site contains supplementary material. Statistics for Spatio-Temporal Data is an excellent book for a graduate-level course on spatio-temporal statistics. It is also a valuable reference for researchers and practitioners in the fields of applied mathematics, engineering, and the environmental and health sciences.
Book Synopsis Hierarchical Modeling and Analysis for Spatial Data by : Sudipto Banerjee
Download or read book Hierarchical Modeling and Analysis for Spatial Data written by Sudipto Banerjee and published by CRC Press. This book was released on 2003-12-17 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the many uses of hierarchical modeling, their application to the statistical analysis of spatial and spatio-temporal data from areas such as epidemiology And environmental science has proven particularly fruitful. Yet to date, the few books that address the subject have been either too narrowly focused on specific aspects of spatial analysis,
Book Synopsis Statistical Modeling for Complex Data by : Bin Sun
Download or read book Statistical Modeling for Complex Data written by Bin Sun and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we focus on statistical modeling techniques for exploring complex data with features such as high dimensionality, nonstationary structure, heavy-tailed distributions, missing data, etc. We study four problems: dimension reduction in high-dimensional data, clarifying complex patterns in nonstationary spatial data, improving hierarchical Bayesian modeling of spatio-temporal data with staircase pattern of missing observations, and detecting change points in spatio-temporal data with outliers and heavy-tailed observations. Sufficient dimension reduction draws a lot of attention in the last twenty years due to the largely increasing dimensions of the covariates. The semiparametric approach to dimension reduction proposed by Ma and Zhu [2012] is a novel and completely different approach to dimension-reduction problems from the existing literature. We present a theoretical result that relaxes a critical condition required by the semiparametric approach. The asymptotic normality of the estimators still maintains under weaker assumptions. This improvement increases the applicability of the semiparametric approach. For spatial data, nonstationarity brings difficulties to learn the underlying processes, more specifically, to find spatial dependency using the semivariogram model. We improve the modeling technique through dimension expansion proposed by Bornn et al. [2012] by considering the correlation structure. We propose two generalized least-squares methods. Both of the methods provide more accurate parameter estimations than the least-squares method, which has been demonstrated through simulation studies and real data analyses. As spatio-temporal data are usually observed over a large area and in many years, modeling spatio-temporal data is non-trivial. Missing data makes the task even more challenging. One of the problems discussed in this dissertation is to model ozone concentrations in a region in the presence of missing data. We propose a method without assumptions on the correlation structure to estimate the covariance matrix through dimension expansion method for modeling the semivariograms in nonstationary fields based on the estimations from the hierarchical Bayesian spatio-temporal modeling technique [Le and Zidek, 2006]. For demonstration, we apply the method in ozone concentrations at 25 stations in the Pittsburgh region studied in Jin et al. [2012]. The comparison of the proposed method and the one in Jin et al. [2012] are provided through leave-one-out cross-validation which shows that the proposed method is more general and applicable. The last problem which is also related to spatio-temporal data is to detect structural changes for spatio-temporal data with missing in the presence of outliers and heavy-tailed observations. We improve the estimation algorithm of a general spatio-temporal autoregressive (GSTAR) model proposed by Wu et al. [2017]. We propose M-estimation-based EM algorithm and change-point detection procedure. Through data examples, we compare the proposed algorithm and the proposed change-point detection procedure with the existing ones and show that our method provides more robust estimation and is more accurate in detecting change points in the presence of outliers and/or heavy-tailed observations.
Book Synopsis Spatio-Temporal Statistics with R by : Christopher K. Wikle
Download or read book Spatio-Temporal Statistics with R written by Christopher K. Wikle and published by CRC Press. This book was released on 2019-02-18 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The world is becoming increasingly complex, with larger quantities of data available to be analyzed. It so happens that much of these "big data" that are available are spatio-temporal in nature, meaning that they can be indexed by their spatial locations and time stamps. Spatio-Temporal Statistics with R provides an accessible introduction to statistical analysis of spatio-temporal data, with hands-on applications of the statistical methods using R Labs found at the end of each chapter. The book: Gives a step-by-step approach to analyzing spatio-temporal data, starting with visualization, then statistical modelling, with an emphasis on hierarchical statistical models and basis function expansions, and finishing with model evaluation Provides a gradual entry to the methodological aspects of spatio-temporal statistics Provides broad coverage of using R as well as "R Tips" throughout. Features detailed examples and applications in end-of-chapter Labs Features "Technical Notes" throughout to provide additional technical detail where relevant Supplemented by a website featuring the associated R package, data, reviews, errata, a discussion forum, and more The book fills a void in the literature and available software, providing a bridge for students and researchers alike who wish to learn the basics of spatio-temporal statistics. It is written in an informal style and functions as a down-to-earth introduction to the subject. Any reader familiar with calculus-based probability and statistics, and who is comfortable with basic matrix-algebra representations of statistical models, would find this book easy to follow. The goal is to give as many people as possible the tools and confidence to analyze spatio-temporal data.
Book Synopsis Statistics for Spatio-Temporal Data by : Noel Cressie
Download or read book Statistics for Spatio-Temporal Data written by Noel Cressie and published by John Wiley & Sons. This book was released on 2015-11-02 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: Winner of the 2013 DeGroot Prize. A state-of-the-art presentation of spatio-temporal processes, bridging classic ideas with modern hierarchical statistical modeling concepts and the latest computational methods Noel Cressie and Christopher K. Wikle, are also winners of the 2011 PROSE Award in the Mathematics category, for the book “Statistics for Spatio-Temporal Data” (2011), published by John Wiley and Sons. (The PROSE awards, for Professional and Scholarly Excellence, are given by the Association of American Publishers, the national trade association of the US book publishing industry.) Statistics for Spatio-Temporal Data has now been reprinted with small corrections to the text and the bibliography. The overall content and pagination of the new printing remains the same; the difference comes in the form of corrections to typographical errors, editing of incomplete and missing references, and some updated spatio-temporal interpretations. From understanding environmental processes and climate trends to developing new technologies for mapping public-health data and the spread of invasive-species, there is a high demand for statistical analyses of data that take spatial, temporal, and spatio-temporal information into account. Statistics for Spatio-Temporal Data presents a systematic approach to key quantitative techniques that incorporate the latest advances in statistical computing as well as hierarchical, particularly Bayesian, statistical modeling, with an emphasis on dynamical spatio-temporal models. Cressie and Wikle supply a unique presentation that incorporates ideas from the areas of time series and spatial statistics as well as stochastic processes. Beginning with separate treatments of temporal data and spatial data, the book combines these concepts to discuss spatio-temporal statistical methods for understanding complex processes. Topics of coverage include: Exploratory methods for spatio-temporal data, including visualization, spectral analysis, empirical orthogonal function analysis, and LISAs Spatio-temporal covariance functions, spatio-temporal kriging, and time series of spatial processes Development of hierarchical dynamical spatio-temporal models (DSTMs), with discussion of linear and nonlinear DSTMs and computational algorithms for their implementation Quantifying and exploring spatio-temporal variability in scientific applications, including case studies based on real-world environmental data Throughout the book, interesting applications demonstrate the relevance of the presented concepts. Vivid, full-color graphics emphasize the visual nature of the topic, and a related FTP site contains supplementary material. Statistics for Spatio-Temporal Data is an excellent book for a graduate-level course on spatio-temporal statistics. It is also a valuable reference for researchers and practitioners in the fields of applied mathematics, engineering, and the environmental and health sciences.
Book Synopsis Predictive Modeling of Spatio-temporal Datasets in High Dimensions by : Linchao Chen
Download or read book Predictive Modeling of Spatio-temporal Datasets in High Dimensions written by Linchao Chen and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Spatio-temporal datasets in many research areas may be very high-dimensional and have complicated dependence structures in both space and time. Various dimension reduction techniques have been introduced to extract key information from single or multiple datasets. Standard dimension-reduced Bayesian hierarchical modeling approaches use a few spatial basis functions to capture the spatial structure and model temporal dynamics through their coefficients. However, these approaches are not always satisfactory in predictive modeling of complicated systems. It is challenging to build statistical models that are computationally efficient for very large datasets and able to adequately model the dependence structure. In this dissertation, we focus on developing modeling strategies for high-dimensional spatio-temporal datasets in the context of predictive modeling, especially when standard dimension reduction methods do not perform well. We discuss modeling strategies to synthesize multiple high-dimensional information sources and produce accurate predictions. We consider the sea surface temperature (SST) prediction problem of Berliner et al. [2000] and demonstrate challenges and advantages of incorporating high-dimensional climate model output along with temperature observations to improve predictive accuracy. Furthermore, we develop a two-scale modeling strategy for dimension-reduced modeling. This modeling strategy is able to capture both large-scale and local dynamics using a large-scale component derived from standard dimension reduction techniques and a local component customized for each pre-partitioned subregion. Empirical experiments show that this strategy is more efficient in capturing variability when standard dimension reduction methods do not perform well. It delivers more balanced results in the presence of outliers. We also discuss its potential as a spatially varying modeling approach. Finally, we gather examples of how one can use coarse scale information in dimension reduction, EOF analysis, predictive modeling, generation of partitions, and provide discussion on potential strategies to choose appropriate aggregation scales.
Book Synopsis Spatio-Temporal Methods in Environmental Epidemiology by : Gavin Shaddick
Download or read book Spatio-Temporal Methods in Environmental Epidemiology written by Gavin Shaddick and published by CRC Press. This book was released on 2015-06-17 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teaches Students How to Perform Spatio-Temporal Analyses within Epidemiological StudiesSpatio-Temporal Methods in Environmental Epidemiology is the first book of its kind to specifically address the interface between environmental epidemiology and spatio-temporal modeling. In response to the growing need for collaboration between statisticians and
Book Synopsis Dimension Reduced Modeling of Spatio-temporal Processes with Applications to Statistical Downscaling by : Jenný Brynjarsdóttir
Download or read book Dimension Reduced Modeling of Spatio-temporal Processes with Applications to Statistical Downscaling written by Jenný Brynjarsdóttir and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: The field of spatial and spatio-temporal statistics is increasingly faced with the challenge of very large datasets. Examples include data obtained from remote sensing satellites, global weather stations, outputs from climate models and medical imagery. The classical approach to spatial and spatio-temporal modeling is extremely computationally expensive when the datasets are large. Dimension-reduced modeling approach has proved to be effective in such situations. In this thesis I focus on the problem of modeling two spatio-temporal processes where the primary goal is to predict one process from the other and where the datasets for both processes are large.
Book Synopsis Handbook of Mathematical Geosciences by : B.S. Daya Sagar
Download or read book Handbook of Mathematical Geosciences written by B.S. Daya Sagar and published by Springer. This book was released on 2018-06-25 with total page 911 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Open Access handbook published at the IAMG's 50th anniversary, presents a compilation of invited path-breaking research contributions by award-winning geoscientists who have been instrumental in shaping the IAMG. It contains 45 chapters that are categorized broadly into five parts (i) theory, (ii) general applications, (iii) exploration and resource estimation, (iv) reviews, and (v) reminiscences covering related topics like mathematical geosciences, mathematical morphology, geostatistics, fractals and multifractals, spatial statistics, multipoint geostatistics, compositional data analysis, informatics, geocomputation, numerical methods, and chaos theory in the geosciences.
Book Synopsis Spatial and Spatio-temporal Bayesian Models with R - INLA by : Marta Blangiardo
Download or read book Spatial and Spatio-temporal Bayesian Models with R - INLA written by Marta Blangiardo and published by John Wiley & Sons. This book was released on 2015-06-02 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spatial and Spatio-Temporal Bayesian Models with R-INLA provides a much needed, practically oriented & innovative presentation of the combination of Bayesian methodology and spatial statistics. The authors combine an introduction to Bayesian theory and methodology with a focus on the spatial and spatio-temporal models used within the Bayesian framework and a series of practical examples which allow the reader to link the statistical theory presented to real data problems. The numerous examples from the fields of epidemiology, biostatistics and social science all are coded in the R package R-INLA, which has proven to be a valid alternative to the commonly used Markov Chain Monte Carlo simulations
Book Synopsis Modeling for Spatial and Spatio-temporal Data with Applications by : Xintong Li
Download or read book Modeling for Spatial and Spatio-temporal Data with Applications written by Xintong Li and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: It is common to assume the spatial or spatio-temporal data are realizations of underlying random fields or stochastic processes. Effective approaches to modeling of the underlying autocorrelation structure of the same random field and the association among multiple processes are of great demand in many areas including atmospheric sciences, meteorology and agriculture. To this end, this dissertation studies methods and application of the spatial modeling of large-scale dependence structure and spatio-temporal regression modelling. First, variogram and variogram matrix functions play important roles in modeling dependence structure among processes at different locations in spatial statistics. With more and more data collected on a global scale in environmental science, geophysics, and related fields, we focus on the characterizations of the variogram models on spheres of all dimensions for both stationary and intrinsic stationary, univariate and multivariate random fields. Some effcient approaches are proposed to construct a variety of variograms including simple polynomial structures. In particular, the series representation and spherical behavior of intrinsic stationary random fields are explored in both theoretical and simulation study. The applications of the proposed model and related theoretical results are demonstrated using simulation and real data analysis. Second, knowledge of the influential factors on the number of days suitable for fieldwork (DSFW) has important implications on timing of agricultural field operations, machinery decision, and risk management. To assess how some global climate phenomena such as El Nino Southern Oscillation (ENSO) affects DSFW and capture their complex associations in space and time, we propose various spatio-temporal dynamic models under hierarchical Bayesian framework. The Integrated Nested Laplace Approximation (INLA) is used and adapted to reduce the computational burden experienced when a large number of geo-locations and time points is considered in the data set. A comparison study between dynamics models with INLA viewing spatial domain as discrete and continuous is conducted and their pros and cons are evaluated based on multiple criteria. Finally a model with time- varying coefficients is shown to reflect the dynamic nature of the impact and lagged effect of ENSO on DSFW in US with spatio-temporal correlations accounted.
Book Synopsis Handbook of Discrete-Valued Time Series by : Richard A. Davis
Download or read book Handbook of Discrete-Valued Time Series written by Richard A. Davis and published by CRC Press. This book was released on 2016-01-06 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model a Wide Range of Count Time Series Handbook of Discrete-Valued Time Series presents state-of-the-art methods for modeling time series of counts and incorporates frequentist and Bayesian approaches for discrete-valued spatio-temporal data and multivariate data. While the book focuses on time series of counts, some of the techniques discussed ca
Book Synopsis Bayesian Modeling of Spatio-Temporal Data with R by : Sujit Sahu
Download or read book Bayesian Modeling of Spatio-Temporal Data with R written by Sujit Sahu and published by CRC Press. This book was released on 2022-02-23 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applied sciences, both physical and social, such as atmospheric, biological, climate, demographic, economic, ecological, environmental, oceanic and political, routinely gather large volumes of spatial and spatio-temporal data in order to make wide ranging inference and prediction. Ideally such inferential tasks should be approached through modelling, which aids in estimation of uncertainties in all conclusions drawn from such data. Unified Bayesian modelling, implemented through user friendly software packages, provides a crucial key to unlocking the full power of these methods for solving challenging practical problems. Key features of the book: • Accessible detailed discussion of a majority of all aspects of Bayesian methods and computations with worked examples, numerical illustrations and exercises • A spatial statistics jargon buster chapter that enables the reader to build up a vocabulary without getting clouded in modeling and technicalities • Computation and modeling illustrations are provided with the help of the dedicated R package bmstdr, allowing the reader to use well-known packages and platforms, such as rstan, INLA, spBayes, spTimer, spTDyn, CARBayes, CARBayesST, etc • Included are R code notes detailing the algorithms used to produce all the tables and figures, with data and code available via an online supplement • Two dedicated chapters discuss practical examples of spatio-temporal modeling of point referenced and areal unit data • Throughout, the emphasis has been on validating models by splitting data into test and training sets following on the philosophy of machine learning and data science This book is designed to make spatio-temporal modeling and analysis accessible and understandable to a wide audience of students and researchers, from mathematicians and statisticians to practitioners in the applied sciences. It presents most of the modeling with the help of R commands written in a purposefully developed R package to facilitate spatio-temporal modeling. It does not compromise on rigour, as it presents the underlying theories of Bayesian inference and computation in standalone chapters, which would be appeal those interested in the theoretical details. By avoiding hard core mathematics and calculus, this book aims to be a bridge that removes the statistical knowledge gap from among the applied scientists.
Book Synopsis Theory of Spatial Statistics by : M.N.M. van Lieshout
Download or read book Theory of Spatial Statistics written by M.N.M. van Lieshout and published by CRC Press. This book was released on 2019-03-19 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Spatial Statistics: A Concise Introduction presents the most important models used in spatial statistics, including random fields and point processes, from a rigorous mathematical point of view and shows how to carry out statistical inference. It contains full proofs, real-life examples and theoretical exercises. Solutions to the latter are available in an appendix. Assuming maturity in probability and statistics, these concise lecture notes are self-contained and cover enough material for a semester course. They may also serve as a reference book for researchers. Features * Presents the mathematical foundations of spatial statistics. * Contains worked examples from mining, disease mapping, forestry, soil and environmental science, and criminology. * Gives pointers to the literature to facilitate further study. * Provides example code in R to encourage the student to experiment. * Offers exercises and their solutions to test and deepen understanding. The book is suitable for postgraduate and advanced undergraduate students in mathematics and statistics.
Book Synopsis Hierarchical Modeling of Spatio-temporally Misaligned Data by : Li Zhu
Download or read book Hierarchical Modeling of Spatio-temporally Misaligned Data written by Li Zhu and published by . This book was released on 2000 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hierarchical Modelling for the Environmental Sciences by : James Samuel Clark
Download or read book Hierarchical Modelling for the Environmental Sciences written by James Samuel Clark and published by Oxford University Press, USA. This book was released on 2006 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: New statistical tools are changing the ways in which scientists analyze and interpret data and models. Many of these are emerging as a result of the wide availability of inexpensive, high speed computational power. In particular, hierarchical Bayes and Markov Chain Monte Carlo methods for analysis provide consistent framework for inference and prediction where information is heterogeneous and uncertain, processes are complex, and responses depend on scale. Nowhere are these methods more promising than in the environmental sciences. Models have developed rapidly, and there is now a requirement for a clear exposition of the methodology through to application for a range of environmental challenges.
