Gaussian Process Regression Analysis for Functional Data

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.

Introduction Functional Regression ModelsGaussian Process Regression Some Data Sets and Associated Statistical Problems Bayesian Nonlinear Regression with Gaussian Process PriorsGaussian Process Prior and PosteriorPosterior ConsistencyAsymptotic Properties of the Gaussian Process Regression Models Inference and Computation for Gaussian Process Regression Model Empirical Bayes Estimates Bayesian Inference and MCMCNumerical Computation Covariance Function and Model SelectionExamples of Covariance FunctionsSelection of Covariance FunctionsVariable 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 GPFR ANOVA Model Mixture Models and Curve ClusteringMixture GPR Models Mixtures of GPFR ModelsCurve Clustering Generalized Gaussian Process Regression for Non-Gaussian Functional DataGaussian Process Binary Regression Model Generalized Gaussian Process RegressionGeneralized GPFR Model for Batch DataMixture Models for Multinomial Batch Data Some Other Related ModelsMultivariate Gaussian Process Regression ModelGaussian Process Latent Variable ModelsOptimal Dynamic Control Using GPR ModelRKHS and Gaussian Process Regression Appendices Bibliography Index 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.