Bayesian Spatial Modelling With Conjugate Prior Models
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Bayesian Spatial Modelling with Conjugate Prior Models
This book offers a comprehensive overview of statistical methodology for modelling and evaluating spatial variables useful in a variety of applications. These spatial variables fall into three categories: continuous, like terrain elevation; events, like tree locations; and mosaics, like medical images. Definitions and discussions of random field models are included for each of these three previously mentioned spatial variable types. Moreover, the readers will have access to algorithms suitable for applying this methodology in practical problem solving, and the computational efficiency of these algorithms are discussed. The presentation is made in a consistent predictive Bayesian framework, which allows separate modelling of the observation acquisition procedure, as a likelihood model, and of the spatial variable characteristics, as a prior spatial model. The likelihood and prior models uniquely define the posterior spatial model, which provides the basis for spatial simulations, spatial predictions with associated precisions, and model parameter inference. The emphasis is on Bayesian spatial modelling with conjugate pairs of likelihood and prior models that are analytically tractable and hence suitable for data abundant spatial studies. Alternative methods frequently used in spatial statistics are presented using a unified notation. The book is suitable as a textbook for a ‘Spatial Statistics’ course at the MSc or PhD level, as it also includes algorithm descriptions, project texts, and exercises.
Bayesian Spatial Modelling with Conjugate Prior Models
"This book offers a comprehensive overview of statistical methodology for modelling and evaluating spatial variables useful in a variety of applications. These spatial variables fall into three categories: continuous, like terrain elevation; events, like tree locations; and mosaics, like medical images. Definitions and discussions of random field models are included for each of these three previously mentioned spatial variable types. Moreover, the readers will have access to algorithms suitable for applying this methodology in practical problem solving, and the computational efficiency of these algorithms are discussed. The presentation is made in a consistent predictive Bayesian framework, which allows separate modelling of the observation acquisition procedure, as a likelihood model, and of the spatial variable characteristics, as a prior spatial model. The likelihood and prior models uniquely define the posterior spatial model, which provides the basis for spatial simulations, spatial predictions with associated precisions, and model parameter inference. The emphasis is on Bayesian spatial modelling with conjugate pairs of likelihood and prior models that are analytically tractable and hence suitable for data abundant spatial studies. Alternative methods frequently used in spatial statistics are presented using a unified notation. The book is suitable as a textbook for a Spatial Statistics course at the MSc or PhD level, as it also includes algorithm descriptions, project texts, and exercises."--
Bayesian Model Selection and Statistical Modeling
Along with many practical applications, Bayesian Model Selection and Statistical Modeling presents an array of Bayesian inference and model selection procedures. It thoroughly explains the concepts, illustrates the derivations of various Bayesian model selection criteria through examples, and provides R code for implementation. The author shows how to implement a variety of Bayesian inference using R and sampling methods, such as Markov chain Monte Carlo. He covers the different types of simulation-based Bayesian model selection criteria, including the numerical calculation of Bayes factors, the Bayesian predictive information criterion, and the deviance information criterion. He also provides a theoretical basis for the analysis of these criteria. In addition, the author discusses how Bayesian model averaging can simultaneously treat both model and parameter uncertainties. Selecting and constructing the appropriate statistical model significantly affect the quality of results in decision making, forecasting, stochastic structure explorations, and other problems. Helping you choose the right Bayesian model, this book focuses on the framework for Bayesian model selection and includes practical examples of model selection criteria.