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Gaussian process regression analysis for functional data

Author: Jian Qing Shi; Taeryon Choi
Publisher: Boca Raton, FL : CRC Press, ©2011.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"Gaussian Process Regression Analysis for Functional Data presents nonparametric statistical methods for functional regression analysis, specifically the methods based on a Gaussian process prior in a functional space. The authors focus on problems involving functional response variables and mixed covariates of functional and scalar variables. Covering the basics of Gaussian process regression, the first several  Read more...
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Details

Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Jian Qing Shi; Taeryon Choi
ISBN: 9781439837733 1439837732
OCLC Number: 491888782
Description: xix, 196 pages : illustrations ; 24 cm
Contents: 1. Introduction: Functional Regression Models --
Gaussian Process Regression --
Some Data Sets and Associated Statistical Problems --
2. Bayesian Nonlinear Regression with Gaussian Process Priors: Gaussian Process Prior and Posterior --
Posterior Consistency --
Asymptotic Properties of the Gaussian Process Regression Models --
3. Inference and Computation for Gaussian Process Regression Model: Empirical Bayes Estimates --
Bayesian Inference and MCMC --
Numerical Computation --
4. Covariance Function and Model Selection: Examples of Covariance Functions --
Selection of Covariance Functions --
Variable Selection --
5. Functional Regression Analysis: Linear Functional Regression Model --
Gaussian Process Functional Regression Model --
GPFR Model with a Linear Functional Mean Model --
Mixed-Effects GPFR Models --
GPFR ANOVA Model --
6. Mixture Models and Curve Clustering: Mixture GPR Models --
Mixtures of GPFR Models --
Curve Clustering --
7. Generalized Gaussian Process Regression for Non-Gaussian Functional Data: Gaussian Process Binary Regression Model --
Generalized Gaussian Process Regression --
Generalized GPFR Model for Batch Data --
Mixture Models for Multinomial Batch Data --
8. Some Other Related Models: Multivariate Gaussian Process Regression Model --
Gaussian Process Latent Variable Models --
Optimal Dynamic Control Using GPR Model --
RKHS and Gaussian Process Regression.
Responsibility: Jian Qing Shi, Taeryon Choi.

Abstract:

"Gaussian Process Regression Analysis for Functional Data presents nonparametric statistical methods for functional regression analysis, specifically the methods based on a Gaussian process prior in a functional space. The authors focus on problems involving functional response variables and mixed covariates of functional and scalar variables. Covering the basics of Gaussian process regression, the first several chapters discuss functional data analysis, theoretical aspects based on the asymptotic properties of Gaussian process regression models, and new methodological developments for high dimensional data and variable selection. The remainder of the text explores advanced topics of functional regression analysis, including novel nonparametric statistical methods for curve prediction, curve clustering, functional ANOVA, and functional regression analysis of batch data, repeated curves, and non-Gaussian data. Many flexible models based on Gaussian processes provide efficient ways of model learning, interpreting model structure, and carrying out inference, particularly when dealing with large dimensional functional data. This book shows how to use these Gaussian process regression models in the analysis of functional data. Some MATLAB® and C codes are available on the first author's website"--Publisher's website.

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