Gaussian Markov Random Fields: Theory and Applications

Gaussian Markov Random Field (GMRF) models are used in spatial statistics, and this book provides a unified framework with computational aspects and extensive case-studies, making it essential reading for statisticians and quantitative researchers in spatial data analysis.

Format: Paperback / softback
Length: 280 pages
Publication date: 21 January 2023
Publisher: Taylor & Francis Ltd

Gaussian Markov Random Field (GMRF) models are widely utilized in spatial statistics, a highly active research domain with limited up-to-date reference materials. This groundbreaking book stands as the first comprehensive treatment of GMRFs, placing particular emphasis on computational aspects. It offers an extensive case-study collection and an online c-library for efficient and precise simulation. Contributions from esteemed experts in the field make this volume an indispensable resource for statisticians engaged in spatial theory and its applications, as well as quantitative researchers across various scientific disciplines where spatial data analysis holds significant importance.

Introduction:
Spatial statistics plays a crucial role in analyzing and understanding spatial data, encompassing a wide range of applications such as geography, ecology, epidemiology, and social sciences. Traditional statistical models, such as linear regression and ordinary least squares, often fail to capture the complex spatial relationships and heterogeneity present in real-world data. As a result, researchers have turned to more advanced models, such as Gaussian Markov Random Field (GMRF) models, to better capture the spatial dependence and randomness of the data.

GMRF Models:
GMRF models are a type of Bayesian non-parametric model that allows for the representation of spatial processes and the modeling of spatial data. They are based on a Markov random field (MRF) framework, which describes the probability distribution of a random variable at each location in a spatial domain. GMRF models can handle a wide range of spatial structures, including point patterns, line patterns, surface patterns, and spatial autocorrelation.

Computational Aspects:
One of the key challenges in using GMRF models is the computational complexity associated with their inference and estimation. Traditional approaches to GMRF modeling involve solving large matrix equations, which can be computationally demanding and time-consuming. However, recent advancements in computational techniques have made it possible to efficiently simulate and analyze GMRF models.

This Book:
This book aims to provide a comprehensive and up-to-date introduction to GMRF models, with a particular emphasis on the computational aspects. It covers the theoretical foundations of GMRF models, including their derivations, properties, and applications. The book also discusses the computational techniques used to simulate and analyze GMRF models, including Markov chain Monte Carlo (MCMC) methods, variational inference, and fast algorithms.

Case Studies:
To illustrate the practical applications of GMRF models, the book includes extensive case-studies drawn from various fields of research. These case studies cover topics such as disease mapping, urban dynamics, land use change, and climate change. The case studies demonstrate how GMRF models can be used to analyze spatial data, identify patterns, and make predictions.

Online C-Library:
In addition to the theoretical and computational aspects, this book also provides an online c-library for fast and exact simulation of GMRF models. The c-library includes a wide range of functions and tools that can be used to simulate and analyze GMRF models, making it easier for researchers to implement and evaluate their models.

Conclusion:
Gaussian Markov Random Field (GMRF) models are a powerful tool for analyzing spatial data and have gained significant popularity in recent years. This book provides a comprehensive and up-to-date introduction to GMRF models, with a particular emphasis on the computational aspects. It offers extensive case-studies and an online c-library for fast and exact simulation, making it an essential resource for statisticians, quantitative researchers, and anyone interested in spatial data analysis.

Weight: 520g
Dimension: 229 x 152 (mm)
ISBN-13: 9781032477909