Bayesian Spatial Modelling with Conjugate Prior Models / by Henning Omre, Torstein M. Fjeldstad, Ole Bernhard Forberg.

Format:

Book

Author/Creator:

Omre, Henning.

Contributor:

Fjeldstad, Torstein M.

Forberg, Ole Bernhard.

Language:

English

Subjects (All):

Statistics.

Geographic information systems.

Bayesian Inference.

Geographical Information System.

Local Subjects:

Bayesian Inference.

Geographical Information System.

Physical Description:

1 online resource (237 pages)

Edition:

1st ed. 2024.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2024.

Summary:

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.

Contents:

- Introduction

Bayesian Spatial Modelling

Conjugate Inversion Models

Random Fields

Part I Traditional Conjugate Spatial Models

Likelihood Models

Prior Models

Posterior Models

Model Parameter Inference

Computational Challenges.

ISBN:

3-031-65418-8