Sudipto Banerjee

Hierarchical Modeling and Analysis for Spatial Data, Third Edition presents a comprehensive and up-to-date treatment of hierarchical and multilevel modeling for spatial and spatio-temporal data within a Bayesian framework. Over the past decade since the second edition, spatial statistics has evolved significantly, driven by an explosion in data availability and advances in Bayesian computation. This edition reflects those changes, introducing new methods, expanded applications, and enhanced computational resources to support researchers and practitioners across disciplines, including environmental science, ecology, and public health. Key features of the third edition:A dedicated chapter on state-of-the-art Bayesian modeling of large spatial and spatio-temporal datasetsTwo new chapters on spatial point pattern analysis, covering both foundational and Bayesian perspectivesA new chapter on spatial data fusion, integrating diverse spatial data sources from different probabilistic mechanismsAn accessible introduction to GPS mapping, geodesic distances, and mathematical cartographyAn expanded special topics chapter, including spatial challenges with finite population modeling and spatial directional dataA thoroughly revised chapter on Bayesian inference, featuring an updated review of modern computational techniquesA dedicated GitHub repository providing R programs and solutions to selected exercises, ensuring continued access to evolving software developmentsWith refreshed content throughout, this edition serves as an essential reference for statisticians, data scientists, and researchers working with spatial data. Graduate students and professionals seeking a deep understanding of Bayesian spatial modeling will find this volume an invaluable resource for both theory and practice.

Keep Up to Date with the Evolving Landscape of Space and Space-Time Data Analysis and ModelingSince the publication of the first edition, the statistical landscape has substantially changed for analyzing space and space-time data. More than twice the size of its predecessor, Hierarchical Modeling and Analysis for Spatial Data, Second Edition reflects the major growth in spatial statistics as both a research area and an area of application. New to the Second Edition New chapter on spatial point patterns developed primarily from a modeling perspectiveNew chapter on big data that shows how the predictive process handles reasonably large datasetsNew chapter on spatial and spatiotemporal gradient modeling that incorporates recent developments in spatial boundary analysis and womblingNew chapter on the theoretical aspects of geostatistical (point-referenced) modeling Greatly expanded chapters on methods for multivariate and spatiotemporal modelingNew special topics sections on data fusion/assimilation and spatial analysis for data on extremesDouble the number of exercises Many more color figures integrated throughout the textUpdated computational aspects, including the latest version of WinBUGS, the new flexible spBayes software, and assorted R packagesThe Only Comprehensive Treatment of the Theory, Methods, and SoftwareThis second edition continues to provide a complete treatment of the theory, methods, and application of hierarchical modeling for spatial and spatiotemporal data. It tackles current challenges in handling this type of data, with increased emphasis on observational data, big data, and the upsurge of associated software tools. The authors also explore important application domains, including environmental science, forestry, public health, and real estate.

Linear Algebra and Matrix Analysis for Statistics offers a gradual exposition to linear algebra without sacrificing the rigor of the subject. It presents both the vector space approach and the canonical forms in matrix theory. The book is as self-contained as possible, assuming no prior knowledge of linear algebra. The authors first address the rudimentary mechanics of linear systems using Gaussian elimination and the resulting decompositions. They introduce Euclidean vector spaces using less abstract concepts and make connections to systems of linear equations wherever possible. After illustrating the importance of the rank of a matrix, they discuss complementary subspaces, oblique projectors, orthogonality, orthogonal projections and projectors, and orthogonal reduction. The text then shows how the theoretical concepts developed are handy in analyzing solutions for linear systems. The authors also explain how determinants are useful for characterizing and deriving properties concerning matrices and linear systems. They then cover eigenvalues, eigenvectors, singular value decomposition, Jordan decomposition (including a proof), quadratic forms, and Kronecker and Hadamard products. The book concludes with accessible treatments of advanced topics, such as linear iterative systems, convergence of matrices, more general vector spaces, linear transformations, and Hilbert spaces.