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Bayesian Smoothing and Regression for Longitudinal, Spatial and Event History Data$
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Ludwig Fahrmeir and Thomas Kneib

Print publication date: 2011

Print ISBN-13: 9780199533022

Published to Oxford Scholarship Online: September 2011

DOI: 10.1093/acprof:oso/9780199533022.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 17 April 2021

Spatial Smoothing, Interactions and Geoadditive Regression

Spatial Smoothing, Interactions and Geoadditive Regression

(p.307) 5 Spatial Smoothing, Interactions and Geoadditive Regression
Bayesian Smoothing and Regression for Longitudinal, Spatial and Event History Data

Ludwig Fahrmeir (Contributor Webpage)

Thomas Kneib (Contributor Webpage)

Oxford University Press

This chapter provides an introduction to Bayesian spatial smoothing as a subject of interest in its own right, it points out the close relation between modelling interactions and spatial effects, and it extends smoothing and regression to geoadditive regression models. Section 5.1 introduces the different types of spatial data in more detail and provides information on the corresponding modelling techniques. Section 5.2 describes Markov random fields as basic stochastic process models for discrete spatial data. Section 5.3 highlights relations between continuous spatial smoothing approaches and the modelling of interactions. Section 5.4 introduces Gaussian random fields as stochastic process models for continuous spatial data, including their use in classical geostatistics. Section 5.5 incorporates ideas from the previous sections in the general framework of geoadditive regression.

Keywords:   Bayesian spatial smoothing, geoadditive regression models, Markov random fields, Gaussian random fields, stochastic process models

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