Download or read book Approximate Profile Likelihood Estimation for Spatial dependence Parameters written by Hongfei Li and published by . This book was released on 2007 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: The problem of accounting for spatial dependence in statistical analyses has received considerable attention due to the prevalence of spatial data in many disciplines. Typically, statistical analyses proceed by first testing if there is spatial dependence in the data. Then, if we find it, we want to measure its strength. Previous studies either do not provide obvious estimators of spatial-dependence parameters in commonly used models, or they cannot be expressed in closed form. For example, maximum likelihood estimators (MLEs) cannot typically be expressed in closed form. In this dissertation, we develop alternative closed-form measures of spatial dependence, which we call APLEs, as they are approximate profile likelihood estimators of parameters in spatial lattice models. While we consider three commonly used spatial lattice models, this dissertation primarily focuses on the APLEs for the simultaneous autoregressive (SAR) model. For this model, we derive APLEs under different scenarios where the nuisance parameters are known or unknown. We include both theoretical and simulation-based motivation (including comparison to the MLE) for using APLE as an estimator, and we explore its asymptotic properties. In conjunction, we propose the APLE scatterplot and local APLEs for assessing the strength of spatial dependence visually and for identifying "spatial outliers". Crime data from Columbus, Ohio are used to illustrate the use of our APLE statistics in exploratory data analyses. In addition to considering the properties of APLE as an estimator of spatial dependence, we show that APLE can be used as a test statistic. Finally, we derive APLEs in the presence of measurement error, as well as heteroskedasticity. Beyond the SAR-based APLE, we also derive APLEs for spatial-dependence parameters in the conditional autoregressive (CAR) and spatial moving-average (SMA) models. To accommodate features of these models, the APLE approach must be modified slightly. The efficiency of the APLEs for these two lattice models is evaluated, and heteroskedasticity extensions are provided.
Download or read book Spatial Statistical Methods for Geography written by Peter A. Rogerson and published by SAGE. This book was released on 2021-03-17 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible new textbook offers a straightforward introduction to doing spatial statistics. Grounded in real world examples, it shows you how to extend traditional statistical methods for use with spatial data. The book assumes basic mathematical and statistics knowledge but also provides a handy refresher guide, so that you can develop your understanding and progress confidently. It also: · Equips you with the tools to both interpret and apply spatial statistical methods · Engages with the unique considerations that apply when working with geographic data · Helps you build your knowledge of key spatial statistical techniques, such as methods of geographic cluster detection.
Download or read book Introduction to Spatial Econometrics written by James LeSage and published by CRC Press. This book was released on 2009-01-20 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although interest in spatial regression models has surged in recent years, a comprehensive, up-to-date text on these approaches does not exist. Filling this void, Introduction to Spatial Econometrics presents a variety of regression methods used to analyze spatial data samples that violate the traditional assumption of independence between observat
Download or read book Spatial AutoRegression SAR Model written by Baris M. Kazar and published by Springer Science & Business Media. This book was released on 2012-03-02 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explosive growth in the size of spatial databases has highlighted the need for spatial data mining techniques to mine the interesting but implicit spatial patterns within these large databases. This book explores computational structure of the exact and approximate spatial autoregression (SAR) model solutions. Estimation of the parameters of the SAR model using Maximum Likelihood (ML) theory is computationally very expensive because of the need to compute the logarithm of the determinant (log-det) of a large matrix in the log-likelihood function. The second part of the book introduces theory on SAR model solutions. The third part of the book applies parallel processing techniques to the exact SAR model solutions. Parallel formulations of the SAR model parameter estimation procedure based on ML theory are probed using data parallelism with load-balancing techniques. Although this parallel implementation showed scalability up to eight processors, the exact SAR model solution still suffers from high computational complexity and memory requirements. These limitations have led the book to investigate serial and parallel approximate solutions for SAR model parameter estimation. In the fourth and fifth parts of the book, two candidate approximate-semi-sparse solutions of the SAR model based on Taylor's Series expansion and Chebyshev Polynomials are presented. Experiments show that the differences between exact and approximate SAR parameter estimates have no significant effect on the prediction accuracy. In the last part of the book, we developed a new ML based approximate SAR model solution and its variants in the next part of the thesis. The new approximate SAR model solution is called the Gauss-Lanczos approximated SAR model solution. We algebraically rank the error of the Chebyshev Polynomial approximation, Taylor's Series approximation and the Gauss-Lanczos approximation to the solution of the SAR model and its variants. In other words, we established a novel relationship between the error in the log-det term, which is the approximated term in the concentrated log-likelihood function and the error in estimating the SAR parameter for all of the approximate SAR model solutions.
Download or read book Separate Estimation of Spatial Dependence Parameters and Variance Parameters in a Spatial Model written by Matthias Arnold and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spatial Linear Models for Environmental Data written by Dale L. Zimmerman and published by CRC Press. This book was released on 2024-04-17 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many applied researchers equate spatial statistics with prediction or mapping, but this book naturally extends linear models, which includes regression and ANOVA as pillars of applied statistics, to achieve a more comprehensive treatment of the analysis of spatially autocorrelated data. Spatial Linear Models for Environmental Data, aimed at students and professionals with a master’s level training in statistics, presents a unique, applied, and thorough treatment of spatial linear models within a statistics framework. Two subfields, one called geostatistics and the other called areal or lattice models, are extensively covered. Zimmerman and Ver Hoef present topics clearly, using many examples and simulation studies to illustrate ideas. By mimicking their examples and R code, readers will be able to fit spatial linear models to their data and draw proper scientific conclusions. Topics covered include: Exploratory methods for spatial data including outlier detection, (semi)variograms, Moran’s I, and Geary’s c. Ordinary and generalized least squares regression methods and their application to spatial data. Suitable parametric models for the mean and covariance structure of geostatistical and areal data. Model-fitting, including inference methods for explanatory variables and likelihood-based methods for covariance parameters. Practical use of spatial linear models including prediction (kriging), spatial sampling, and spatial design of experiments for solving real world problems. All concepts are introduced in a natural order and illustrated throughout the book using four datasets. All analyses, tables, and figures are completely reproducible using open-source R code provided at a GitHub site. Exercises are given at the end of each chapter, with full solutions provided on an instructor’s FTP site supplied by the publisher.
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2008 with total page 902 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Maximum Likelihood Estimation for Sample Surveys written by Raymond L. Chambers and published by CRC Press. This book was released on 2012-05-02 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sample surveys provide data used by researchers in a large range of disciplines to analyze important relationships using well-established and widely used likelihood methods. The methods used to select samples often result in the sample differing in important ways from the target population and standard application of likelihood methods can lead to
Download or read book KriMI A Multiple Imputation Approach for Preserving Spatial Dependencies written by Sara Bleninger and published by University of Bamberg Press. This book was released on 2018-01-25 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Composite Likelihood Estimation and Inference for Spatial Data Models written by Xiaoping Feng and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proportions including exact zero and/or one values observed at spatial locations in a study area are often encountered in environmental and ecological studies. Moreover, for a study with multivariate responses, some response types are often absent at certain sampling locations. A motivating example is a study conducted to assess the influence of social, economic, and historical factors on forest covers. In this thesis, I consider the statistical analysis of this type of problem in a spatial proportional data setting for univariate response and a compositional data setting for multivariate responses, and develop new methodology and theory for this purpose. We first consider a spatial ordered probit model for analyzing spatial ordinal responses with two or more ordered categories and further, a spatial Tobit model for spatial proportional data with zero/one values. A simulation study is conducted to evaluate the performance of the proposed methods, followed by a real ecological data example. Further, we propose a new spatial beta-Bernoulli mixture model and a novel spatial generalized Tobit model which extends an existing spatial Tobit model by applying an inverse beta cumulative distribution function transformation. Simulation studies show that both models are more flexible to capture a variety of shapes of the data distributions compared to the spatial Tobit model. Common studies of compositional data analyze positive random vectors that are subject to a unit-sum constraint. Under the multivariate responses setting, we first propose a practical spatial multivariate ordered probit model for the multivariate ordinal data, where the response variables are discretized nonnegative compositions. In addition, we propose a novel spatial mixture Dirichlet regression model to analyze the spatial dependence and the presence of exact zero values in the first stage, and the nonzero compositional data in the second stage. The parameter estimates for each model are obtained by maximizing a composite likelihood function via a quasi-Newton algorithm. The asymptotic properties of the maximum composite likelihood estimates are established under suitable regularity conditions. An estimate of the inverse of the Godambe information matrix is used for computing the standard errors and the computation is further expedited by parallel computing.
Download or read book Case Studies in Spatial Point Process Modeling written by Adrian Baddeley and published by Springer Science & Business Media. This book was released on 2006-03-03 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Statistical Methods for Spatial Data Analysis written by Oliver Schabenberger and published by CRC Press. This book was released on 2017-01-27 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding spatial statistics requires tools from applied and mathematical statistics, linear model theory, regression, time series, and stochastic processes. It also requires a mindset that focuses on the unique characteristics of spatial data and the development of specialized analytical tools designed explicitly for spatial data analysis. Statistical Methods for Spatial Data Analysis answers the demand for a text that incorporates all of these factors by presenting a balanced exposition that explores both the theoretical foundations of the field of spatial statistics as well as practical methods for the analysis of spatial data. This book is a comprehensive and illustrative treatment of basic statistical theory and methods for spatial data analysis, employing a model-based and frequentist approach that emphasizes the spatial domain. It introduces essential tools and approaches including: measures of autocorrelation and their role in data analysis; the background and theoretical framework supporting random fields; the analysis of mapped spatial point patterns; estimation and modeling of the covariance function and semivariogram; a comprehensive treatment of spatial analysis in the spectral domain; and spatial prediction and kriging. The volume also delivers a thorough analysis of spatial regression, providing a detailed development of linear models with uncorrelated errors, linear models with spatially-correlated errors and generalized linear mixed models for spatial data. It succinctly discusses Bayesian hierarchical models and concludes with reviews on simulating random fields, non-stationary covariance, and spatio-temporal processes. Additional material on the CRC Press website supplements the content of this book. The site provides data sets used as examples in the text, software code that can be used to implement many of the principal methods described and illustrated, and updates to the text itself.
Download or read book Recent Advances and Trends in Nonparametric Statistics written by M.G. Akritas and published by Elsevier. This book was released on 2003-10-31 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: The advent of high-speed, affordable computers in the last two decades has given a new boost to the nonparametric way of thinking. Classical nonparametric procedures, such as function smoothing, suddenly lost their abstract flavour as they became practically implementable. In addition, many previously unthinkable possibilities became mainstream; prime examples include the bootstrap and resampling methods, wavelets and nonlinear smoothers, graphical methods, data mining, bioinformatics, as well as the more recent algorithmic approaches such as bagging and boosting. This volume is a collection of short articles - most of which having a review component - describing the state-of-the art of Nonparametric Statistics at the beginning of a new millennium. Key features: . algorithic approaches . wavelets and nonlinear smoothers . graphical methods and data mining . biostatistics and bioinformatics . bagging and boosting . support vector machines . resampling methods
Download or read book Statistical Methods in Spatial Epidemiology written by Andrew B. Lawson and published by John Wiley & Sons. This book was released on 2013-07-08 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spatial epidemiology is the description and analysis of the geographical distribution of disease. It is more important now than ever, with modern threats such as bio-terrorism making such analysis even more complex. This second edition of Statistical Methods in Spatial Epidemiology is updated and expanded to offer a complete coverage of the analysis and application of spatial statistical methods. The book is divided into two main sections: Part 1 introduces basic definitions and terminology, along with map construction and some basic models. This is expanded upon in Part II by applying this knowledge to the fundamental problems within spatial epidemiology, such as disease mapping, ecological analysis, disease clustering, bio-terrorism, space-time analysis, surveillance and infectious disease modelling. Provides a comprehensive overview of the main statistical methods used in spatial epidemiology. Updated to include a new emphasis on bio-terrorism and disease surveillance. Emphasizes the importance of space-time modelling and outlines the practical application of the method. Discusses the wide range of software available for analyzing spatial data, including WinBUGS, SaTScan and R, and features an accompanying website hosting related software. Contains numerous data sets, each representing a different approach to the analysis, and provides an insight into various modelling techniques. This text is primarily aimed at medical statisticians, researchers and practitioners from public health and epidemiology. It is also suitable for postgraduate students of statistics and epidemiology, as well professionals working in government agencies.
Download or read book Population Parameters written by Hamish McCallum and published by John Wiley & Sons. This book was released on 2008-04-15 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ecologists and environmental managers rely on mathematical models, both to understand ecological systems and to predict future system behavior. In turn, models rely on appropriate estimates of their parameters. This book brings together a diverse and scattered literature, to provide clear guidance on how to estimate parameters for models of animal populations. It is not a recipe book of statistical procedures. Instead, it concentrates on how to select the best approach to parameter estimation for a particular problem, and how to ensure that the quality estimated is the appropriate one for the specific purpose of the modelling exercise. Commencing with a toolbox of useful generic approaches to parameter estimation, the book deals with methods for estimating parameters for single populations. These parameters include population size, birth and death rates, and the population growth rate. For such parameters, rigorous statistical theory has been developed, and software is readily available. The problem is to select the optimal sampling design and method of analysis. The second part of the book deals with parameters that describe spatial dynamics, and ecological interactions such as competition, predation and parasitism. Here the principle problems are designing appropriate experiments and ensuring that the quantities measured by the experiments are relevant to the ecological models in which they will be used. This book will be essential reading for ecological researchers, postgraduate students and environmental managers who need to address an ecological problem through a population model. It is accessible to anyone with an understanding of basic statistical methods and population ecology. Unique in concentrating on parameter estimation within modelling. Fills a glaring gap in the literature. Not too technical, so suitable for the statistically inept. Methods explained in algebra, but also in worked examples using commonly available computer packages (SAS, GLIM, and some more specialised packages where relvant). Some spreadsheet based examples also included.
Download or read book Approximation to the Determinant Term in Maximum Likelihood Estimation of Gaussian Spatial Models written by R. J. Martin and published by . This book was released on 1991 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book In All Likelihood written by Yudi Pawitan and published by OUP Oxford. This book was released on 2013-01-17 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a course in the theory of statistics this text concentrates on what can be achieved using the likelihood/Fisherian method of taking account of uncertainty when studying a statistical problem. It takes the concept ot the likelihood as providing the best methods for unifying the demands of statistical modelling and the theory of inference. Every likelihood concept is illustrated by realistic examples, which are not compromised by computational problems. Examples range from a simile comparison of two accident rates, to complex studies that require generalised linear or semiparametric modelling. The emphasis is that the likelihood is not simply a device to produce an estimate, but an important tool for modelling. The book generally takes an informal approach, where most important results are established using heuristic arguments and motivated with realistic examples. With the currently available computing power, examples are not contrived to allow a closed analytical solution, and the book can concentrate on the statistical aspects of the data modelling. In addition to classical likelihood theory, the book covers many modern topics such as generalized linear models and mixed models, non parametric smoothing, robustness, the EM algorithm and empirical likelihood.
