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Spatial Cluster Modelling

Spatial Cluster Modelling Author Andrew B. Lawson
ISBN-10 9781420035414
Release 2002-05-16
Pages 304
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Research has generated a number of advances in methods for spatial cluster modelling in recent years, particularly in the area of Bayesian cluster modelling. Along with these advances has come an explosion of interest in the potential applications of this work, especially in epidemiology and genome research. In one integrated volume, this book reviews the state-of-the-art in spatial clustering and spatial cluster modelling, bringing together research and applications previously scattered throughout the literature. It begins with an overview of the field, then presents a series of chapters that illuminate the nature and purpose of cluster modelling within different application areas, including astrophysics, epidemiology, ecology, and imaging. The focus then shifts to methods, with discussions on point and object process modelling, perfect sampling of cluster processes, partitioning in space and space-time, spatial and spatio-temporal process modelling, nonparametric methods for clustering, and spatio-temporal cluster modelling. Many figures, some in full color, complement the text, and a single section of references cited makes it easy to locate source material. Leading specialists in the field of cluster modelling authored each chapter, and an introduction by the editors to each chapter provides a cohesion not typically found in contributed works. Spatial Cluster Modelling thus offers a singular opportunity to explore this exciting new field, understand its techniques, and apply them in your own research.

Robust Cluster Analysis and Variable Selection

Robust Cluster Analysis and Variable Selection Author Gunter Ritter
ISBN-10 9781439857960
Release 2014-09-02
Pages 392
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Clustering remains a vibrant area of research in statistics. Although there are many books on this topic, there are relatively few that are well founded in the theoretical aspects. In Robust Cluster Analysis and Variable Selection, Gunter Ritter presents an overview of the theory and applications of probabilistic clustering and variable selection, synthesizing the key research results of the last 50 years. The author focuses on the robust clustering methods he found to be the most useful on simulated data and real-time applications. The book provides clear guidance for the varying needs of both applications, describing scenarios in which accuracy and speed are the primary goals. Robust Cluster Analysis and Variable Selection includes all of the important theoretical details, and covers the key probabilistic models, robustness issues, optimization algorithms, validation techniques, and variable selection methods. The book illustrates the different methods with simulated data and applies them to real-world data sets that can be easily downloaded from the web. This provides you with guidance in how to use clustering methods as well as applicable procedures and algorithms without having to understand their probabilistic fundamentals.

Spatial Statistics and Computational Methods

Spatial Statistics and Computational Methods Author Jesper Møller
ISBN-10 9780387218113
Release 2013-04-17
Pages 205
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This volume shows how sophisticated spatial statistical and computational methods apply to a range of problems of increasing importance for applications in science and technology. It introduces topics of current interest in spatial and computational statistics, which should be accessible to postgraduate students as well as to experienced statistical researchers.

Statistical Analysis of Spatial and Spatio Temporal Point Patterns Third Edition

Statistical Analysis of Spatial and Spatio Temporal Point Patterns  Third Edition Author Peter J. Diggle
ISBN-10 9781466560246
Release 2013-07-23
Pages 268
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Written by a prominent statistician and author, the first edition of this bestseller broke new ground in the then emerging subject of spatial statistics with its coverage of spatial point patterns. Retaining all the material from the second edition and adding substantial new material, Statistical Analysis of Spatial and Spatio-Temporal Point Patterns, Third Edition presents models and statistical methods for analyzing spatially referenced point process data. Reflected in the title, this third edition now covers spatio-temporal point patterns. It explores the methodological developments from the last decade along with diverse applications that use spatio-temporally indexed data. Practical examples illustrate how the methods are applied to analyze spatial data in the life sciences. This edition also incorporates the use of R through several packages dedicated to the analysis of spatial point process data. Sample R code and data sets are available on the author’s website.

Topics in Modelling of Clustered Data

Topics in Modelling of Clustered Data Author Marc Aerts
ISBN-10 9781420035889
Release 2002-05-29
Pages 336
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Many methods for analyzing clustered data exist, all with advantages and limitations in particular applications. Compiled from the contributions of leading specialists in the field, Topics in Modelling of Clustered Data describes the tools and techniques for modelling the clustered data often encountered in medical, biological, environmental, and social science studies. It focuses on providing a comprehensive treatment of marginal, conditional, and random effects models using, among others, likelihood, pseudo-likelihood, and generalized estimating equations methods. The authors motivate and illustrate all aspects of these models in a variety of real applications. They discuss several variations and extensions, including individual-level covariates and combined continuous and discrete outcomes. Flexible modelling with fractional and local polynomials, omnibus lack-of-fit tests, robustification against misspecification, exact, and bootstrap inferential procedures all receive extensive treatment. The applications discussed center primarily, but not exclusively, on developmental toxicity, which leads naturally to discussion of other methodologies, including risk assessment and dose-response modelling. Clearly written, Topics in Modelling of Clustered Data offers a practical, easily accessible survey of important modelling issues. Overview models give structure to a multitude of approaches, figures help readers visualize model characteristics, and a generous use of examples illustrates all aspects of the modelling process.

Case Studies in Spatial Point Process Modeling

Case Studies in Spatial Point Process Modeling Author Adrian Baddeley
ISBN-10 9780387311449
Release 2006-03-03
Pages 310
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Point process statistics is successfully used in fields such as material science, human epidemiology, social sciences, animal epidemiology, biology, and seismology. Its further application depends greatly on good software and instructive case studies that show the way to successful work. This book satisfies this need by a presentation of the spatstat package and many statistical examples. Researchers, spatial statisticians and scientists from biology, geosciences, materials sciences and other fields will use this book as a helpful guide to the application of point process statistics. No other book presents so many well-founded point process case studies. From the reviews: "For those interested in analyzing their spatial data, the wide variatey of examples and approaches here give a good idea of the possibilities and suggest reasonable paths to explore." Michael Sherman for the Journal of the American Statistical Association, December 2006

Medical Applications of Finite Mixture Models

Medical Applications of Finite Mixture Models Author Peter Schlattmann
ISBN-10 9783540686514
Release 2009-03-02
Pages 246
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Patients are not alike! This simple truth is often ignored in the analysis of me- cal data, since most of the time results are presented for the “average” patient. As a result, potential variability between patients is ignored when presenting, e.g., the results of a multiple linear regression model. In medicine there are more and more attempts to individualize therapy; thus, from the author’s point of view biostatis- cians should support these efforts. Therefore, one of the tasks of the statistician is to identify heterogeneity of patients and, if possible, to explain part of it with known explanatory covariates. Finite mixture models may be used to aid this purpose. This book tries to show that there are a large range of applications. They include the analysis of gene - pression data, pharmacokinetics, toxicology, and the determinants of beta-carotene plasma levels. Other examples include disease clustering, data from psychophysi- ogy, and meta-analysis of published studies. The book is intended as a resource for those interested in applying these methods.

Statistical Challenges in Modern Astronomy IV

Statistical Challenges in Modern Astronomy IV Author Gutti Jogesh Babu
ISBN-10 1583812407
Release 2007-01-01
Pages 448
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"This is the fourth in a series of international conferences for the vanguard of researchers in the cross-disciplinary field of astrostatistics. Both astronomical and statistical communities now recognize the wide array of fascinating methodological issues faced by the modern astronomer. Ranging from terabyte wide-field surveys to small-N samples, from cosmology to the search for Earth-like planets, astronomical research can no longer be pursued with a small toolbox of familiar statistical methods. Over thirty distinguished scholars from both fields presented invited talks and commentaries on leading problems in astrostatistics. The methodological challenges of inferring cosmological insights from the cosmic microwave background fluctuations, the distribution of galaxies in space, gravitational lensing, and galaxy structure wre describe in detail. Time series analysis is discussed in a variety of contexts: sparse Poisson data, multiply-periodic systems, gravitational wave detection, and most dramatically in the search for extrasolar planets. Here sophisticated Bayesian model selection with MCMC computations plays a critical role. Other topics covered include image processing, analysis of mega-datasets from large surveys, and small-N problems in both astronomy and particle physics. The volume ends with cross-disciplinary overviews and software tutorials. The book will be valuable to graduate students and researchers in both astronomy and statistics who seek insights into this promising avenue of cross-disciplinary research."--Publisher's website.

Applied Spatial Statistics for Public Health Data

Applied Spatial Statistics for Public Health Data Author Lance A. Waller
ISBN-10 0471662674
Release 2004-07-29
Pages 520
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An application-based introduction to the statistical analysis of spatially referenced health data Sparked by the growing interest in statistical methods for the analysis of spatially referenced data in the field of public health, Applied Spatial Statistics for Public Health Data fills the need for an introductory, application-oriented text on this timely subject. Written for practicing public health researchers as well as graduate students in related fields, the text provides a thorough introduction to basic concepts and methods in applied spatial statistics as well as a detailed treatment of some of the more recent methods in spatial statistics useful for public health studies that have not been previously covered elsewhere. Assuming minimal knowledge of spatial statistics, the authors provide important statistical approaches for assessing such questions as: Are newly occurring cases of a disease "clustered" in space? Do the cases cluster around suspected sources of increased risk, such as toxic waste sites or other environmental hazards? How do we take monitored pollution concentrations measured at specific locations and interpolate them to locations where no measurements were taken? How do we quantify associations between local disease rates and local exposures? After reviewing traditional statistical methods used in public health research, the text provides an overview of the basic features of spatial data, illustrates various geographic mapping and visualization tools, and describes the sources of publicly available spatial data that might be useful in public health applications.

Gaussian Markov Random Fields

Gaussian Markov Random Fields Author Havard Rue
ISBN-10 0203492021
Release 2005-02-18
Pages 280
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Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studies and, online, a c-library for fast and exact simulation. With chapters contributed by leading researchers in the field, this volume is essential reading for statisticians working in spatial theory and its applications, as well as quantitative researchers in a wide range of science fields where spatial data analysis is important.

Statistical Learning with Sparsity

Statistical Learning with Sparsity Author Trevor Hastie
ISBN-10 9781498712170
Release 2015-05-07
Pages 367
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Discover New Methods for Dealing with High-Dimensional Data A sparse statistical model has only a small number of nonzero parameters or weights; therefore, it is much easier to estimate and interpret than a dense model. Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underlying signal in a set of data. Top experts in this rapidly evolving field, the authors describe the lasso for linear regression and a simple coordinate descent algorithm for its computation. They discuss the application of l1 penalties to generalized linear models and support vector machines, cover generalized penalties such as the elastic net and group lasso, and review numerical methods for optimization. They also present statistical inference methods for fitted (lasso) models, including the bootstrap, Bayesian methods, and recently developed approaches. In addition, the book examines matrix decomposition, sparse multivariate analysis, graphical models, and compressed sensing. It concludes with a survey of theoretical results for the lasso. In this age of big data, the number of features measured on a person or object can be large and might be larger than the number of observations. This book shows how the sparsity assumption allows us to tackle these problems and extract useful and reproducible patterns from big datasets. Data analysts, computer scientists, and theorists will appreciate this thorough and up-to-date treatment of sparse statistical modeling.

Statistical Inference and Simulation for Spatial Point Processes

Statistical Inference and Simulation for Spatial Point Processes Author Jesper Moller
ISBN-10 0203496930
Release 2003-09-25
Pages 320
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Spatial point processes play a fundamental role in spatial statistics and today they are an active area of research with many new applications. Although other published works address different aspects of spatial point processes, most of the classical literature deals only with nonparametric methods, and a thorough treatment of the theory and applications of simulation-based inference is difficult to find. Written by researchers at the top of the field, this book collects and unifies recent theoretical advances and examples of applications. The authors examine Markov chain Monte Carlo algorithms and explore one of the most important recent developments in MCMC: perfect simulation procedures.

Point Processes

Point Processes Author D.R. Cox
ISBN-10 0412219107
Release 1980-07-17
Pages 188
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Theoretical framework; Special models; Operations on point processes; Multivariate point processes; Spatial processes.

Stochastic Geometry

Stochastic Geometry Author A. Baddeley
ISBN-10 9783540381754
Release 2006-10-26
Pages 292
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Stochastic Geometry is the mathematical discipline which studies mathematical models for random geometric structures. This book collects lectures presented at the CIME summer school in Martina Franca in September 2004. The main lecturers covered Spatial Statistics, Random Points, Integral Geometry and Random Sets. These are complemented by two additional contributions on Random Mosaics and Crystallization Processes. The book presents a comprehensive and up-to-date description of important aspects of Stochastic Geometry.

Mathematical Reviews

Mathematical Reviews Author
ISBN-10 UOM:39015078588632
Release 2008
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Mathematical Reviews has been writing in one form or another for most of life. You can find so many inspiration from Mathematical Reviews also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Mathematical Reviews book for free.

Bayesian statistical modelling

Bayesian statistical modelling Author Peter Congdon
ISBN-10 0471496006
Release 2001-05-02
Pages 531
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Bayesian methods draw upon previous research findings and combine them with sample data to analyse problems and modify existing hypotheses. The calculations are often extremely complex, with many only now possible due to recent advances in computing technology. Bayesian methods have as a result gained wider acceptance, and are applied in many scientific disciplines, including applied statistics, public health research, medical science, the social sciences and economics. Bayesian Statistical Modelling presents an accessible overview of modelling applications from a Bayesian perspective. * Provides an integrated presentation of theory, examples and computer algorithms * Examines model fitting in practice using Bayesian principles * Features a comprehensive range of methodologies and modelling techniques * Covers recent innovations in bayesian modelling, including Markov Chain Monte Carlo methods * Includes extensive applications to health and social sciences * Features a comprehensive collection of nearly 200 worked examples * Data examples and computer code in WinBUGS are available via ftp Whilst providing a general overview of Bayesian modelling, the author places emphasis on the principles of prior selection, model identification and interpretation of findings, in a range of modelling innovations, focussing on their implementation with real data, with advice as to appropriate computing choices and strategies. Researchers in applied statistics, medical science, public health and the social sciences will benefit greatly from the examples and applications featured. The book will also appeal to graduate students of applied statistics, data analysis and Bayesian methods, and will provide a good reference source for both researchers and students.

The Random Cluster Model

The Random Cluster Model Author Geoffrey R. Grimmett
ISBN-10 9783540328919
Release 2006-12-13
Pages 378
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The random-cluster model has emerged as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. The Random-Cluster Model contains accounts of the subcritical and supercritical phases, together with clear statements of important open problems. The book includes treatment of the first-order (discontinuous) phase transition.