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.
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
Asymptotic Properties of the Gaussian Process Regression Models
Inference and Computation for Gaussian Process Regression Model
Empirical Bayes Estimates
Bayesian Inference and MCMC
Covariance Function and Model Selection
Examples of Covariance Functions
Selection of Covariance Functions
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
Mixture Models and Curve Clustering
Mixture GPR Models
Mixtures of GPFR Models
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.
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.