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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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Basic Concepts for Smoothing and Semiparametric Regression

Basic Concepts for Smoothing and Semiparametric Regression

Chapter:
(p.18) 2 Basic Concepts for Smoothing and Semiparametric Regression
Source:
Bayesian Smoothing and Regression for Longitudinal, Spatial and Event History Data
Author(s):

Ludwig Fahrmeir

Thomas Kneib

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199533022.003.0002

This chapter reviews basic concepts for smoothing and semiparametric regression based on roughness penalties or — from a Bayesian perspective — corresponding smoothness priors. In particular, it introduces several tools for statistical modelling and inference that will be utilized in later chapters. It also highlights the close relation between frequentist penalized likelihood approaches and Bayesian inference based on smoothness priors. The chapter is organized as follows. Section 2.1 considers the classical smoothing problem for time series of Gaussian and non-Gaussian observations. Section 2.2 introduces penalized splines and their Bayesian counterpart as a computationally and conceptually attractive alternative to random-walk priors. Section 2.3 extends the univariate smoothing approaches to additive and generalized additive models.

Keywords:   smoothing, Bayesian inference, Gaussian observation models, non-Gaussian observation models, penalized splines, additive models

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