spatial autoregression sar model parameter estimation techniques

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Spatial Autoregression Sar Model

Author : Baris M. Kazar
ISBN : 9781461418429
Genre : Computers
File Size : 59. 47 MB
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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.

Northstar A Parameter Estimation Method For The Spatial Autoregression Model

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ISBN : OCLC:227926296
Genre :
File Size : 33. 73 MB
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Parameter estimation method for the spatial autoregression model (SAR) is important because of the many application domains, such as regional economics, ecology, environmental management, public safety, transportation, public health, business, travel and tourism. However, it is computationally very expensive because of the need to compute the determinant of a large matrix due to Maximum Likelihood Theory. The limitation of previous studies is the need for numerous computations of the computationally expensive determinant term of the likelihood function. In this paper, we present a faster, scalable and NOvel pRediction and estimation TecHnique for the exact SpaTial Auto Regression model solution (NORTHSTAR). We provide a proof of the correctness of this algorithm by showing the objective function to be unimodular. Analytical and experimental results show that the NORTHSTAR algorithm is computationally faster than the related approaches, because it reduces the number of evaluations of the determinant term in the likelihood function.

The Sage Handbook Of Spatial Analysis

Author : A Stewart Fotheringham
ISBN : 9781446206508
Genre : Social Science
File Size : 50. 37 MB
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The widespread use of Geographical Information Systems (GIS) has significantly increased the demand for knowledge about spatial analytical techniques across a range of disciplines. As growing numbers of researchers realise they are dealing with spatial data, the demand for specialised statistical and mathematical methods designed to deal with spatial data is undergoing a rapid increase. Responding to this demand, The Handbook of Spatial Analysis is a comprehensive and authoritative discussion of issues and techniques in the field of Spatial Data Analysis. Its principal focus is on: • why the analysis of spatial data needs separate treatment • the main areas of spatial analysis • the key debates within spatial analysis • examples of the application of various spatial analytical techniques • problems in spatial analysis • areas for future research Aimed at an international audience of academics, The Handbook of Spatial Analysis will also prove essential to graduate level students and researchers in government agencies and the private sector.

The Handbook Of Geographic Information Science

Author : John P. Wilson
ISBN : 9780470766538
Genre : Science
File Size : 87. 36 MB
Format : PDF
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This Handbook is an essential reference and a guide to the rapidly expanding field of Geographic Information Science. Designed for students and researchers who want an in-depth treatment of the subject, including background information Comprises around 40 substantial essays, each written by a recognized expert in a particular area Covers the full spectrum of research in GIS Surveys the increasing number of applications of GIS Predicts how GIS is likely to evolve in the near future

Spatial Data Analysis

Author : Manfred M. Fischer
ISBN : 3642217206
Genre : Business & Economics
File Size : 39. 28 MB
Format : PDF
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The availability of spatial databases and widespread use of geographic information systems has stimulated increasing interest in the analysis and modelling of spatial data. Spatial data analysis focuses on detecting patterns, and on exploring and modelling relationships between them in order to understand the processes responsible for their emergence. In this way, the role of space is emphasised, and our understanding of the working and representation of space, spatial patterns, and processes is enhanced. In applied research, the recognition of the spatial dimension often yields different and more meaningful results and helps to avoid erroneous conclusions. This book aims to provide an introduction into spatial data analysis to graduates interested in applied statistical research. The text has been structured from a data-driven rather than a theory-based perspective, and focuses on those models, methods and techniques which are both accessible and of practical use for graduate students. Exploratory techniques as well as more formal model-based approaches are presented, and both area data and origin-destination flow data are considered.

Geospatial Analysis

Author : Michael John De Smith
ISBN : 9781905886609
Genre : Mathematics
File Size : 74. 58 MB
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Addresses a range of analytical techniques that are provided within modern Geographic Information Systems and related geospatial software products. This guide covers: the principal concepts of geospatial analysis; core components of geospatial analysis; and, surface analysis, including surface form analysis, gridding and interpolation methods.

Spatial Autocorrelation And Spatial Filtering

Author : Daniel A. Griffith
ISBN : 3540009329
Genre : Business & Economics
File Size : 56. 60 MB
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Exploiting the old maxim that "a picture is worth a thousand words," scientific visualization may be defined as the transformation of numerical scientific data into informative graphical displays. It introduces a nonverbal model into subdisciplines that hitherto employed mostly or only mathematical or verbal-conceptual models. The focus of this monograph is on how scientific visualization can help revolutionize the manner in which the tendencies for (dis)similar numerical values to cluster together in location on a map are explored and analyzed, affording spatial data analyses that are better understood, presented, and used. In doing so, the concept known as spatial autocorrelation - which characterizes these tendencies and is one of the key features of georeferenced data, or data tagged to the earth's surface - is further de-mystified. This self-correlation arises from relative locations in geographic space.

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