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Gaussian Process Regression Analysis for Functional Data


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Table of Contents

Functional Regression Models
Gaussian Process Regression
Some Data Sets and Associated Statistical Problems

Bayesian Nonlinear Regression with Gaussian Process Priors
Gaussian Process Prior and Posterior
Posterior Consistency
Asymptotic Properties of the Gaussian Process Regression Models

Inference and Computation for Gaussian Process Regression Model
Empirical Bayes Estimates
Bayesian Inference and MCMC
Numerical Computation

Covariance Function and Model Selection
Examples of Covariance Functions
Selection of Covariance Functions
Variable Selection

Functional Regression Analysis
Linear Functional Regression Model
Gaussian Process Functional Regression Model
GPFR Model with a Linear Functional Mean Model
Mixed-Effects GPFR Models

Mixture Models and Curve Clustering
Mixture GPR Models
Mixtures of GPFR Models
Curve Clustering

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

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




Further Reading and Notes appear at the end of each chapter.

About the Author

Jian Qing Shi, Ph.D., is a senior lecturer in statistics and the leader of the Applied Statistics and Probability Group at Newcastle University. He is a fellow of the Royal Statistical Society and associate editor of the Journal of the Royal Statistical Society (Series C). His research interests encompass functional data analysis using covariance kernel, incomplete data and model uncertainty, and covariance structural analysis and latent variable models. Taeryon Choi, Ph.D., is an associate professor of statistics at Korea University. His research mainly focuses on the use of Bayesian methods and theory for various scientific problems.

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