Gaussian Process Regression Analysis For Functional Data

Author : Jian Qing Shi,Taeryon Choi
Publisher : CRC Press
Page : 218 pages
File Size : 50,9 Mb
Release : 2011-07-01
Category : Mathematics
ISBN : 9781439837733

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Gaussian Process Regression Analysis for Functional Data by Jian Qing Shi,Taeryon Choi Pdf

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.

Author : James Ramsay,Giles Hooker,Spencer Graves
Publisher : Springer Science & Business Media
Page : 213 pages
File Size : 40,6 Mb
Release : 2009-06-29
Category : Computers
ISBN : 9780387981857

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Functional Data Analysis with R and MATLAB by James Ramsay,Giles Hooker,Spencer Graves Pdf

The book provides an application-oriented overview of functional analysis, with extended and accessible presentations of key concepts such as spline basis functions, data smoothing, curve registration, functional linear models and dynamic systems Functional data analysis is put to work in a wide a range of applications, so that new problems are likely to find close analogues in this book The code in R and Matlab in the book has been designed to permit easy modification to adapt to new data structures and research problems

Author : Carl Edward Rasmussen,Christopher K. I. Williams
Publisher : MIT Press
Page : 266 pages
File Size : 47,8 Mb
Release : 2005-11-23
Category : Computers
ISBN : 9780262182539

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Gaussian Processes for Machine Learning by Carl Edward Rasmussen,Christopher K. I. Williams Pdf

A comprehensive and self-contained introduction to Gaussian processes, which provide a principled, practical, probabilistic approach to learning in kernel machines. Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics. The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes.

Author : Piotr Kokoszka,Matthew Reimherr
Publisher : CRC Press
Page : 311 pages
File Size : 43,5 Mb
Release : 2017-09-27
Category : Mathematics
ISBN : 9781498746694

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Introduction to Functional Data Analysis by Piotr Kokoszka,Matthew Reimherr Pdf

Introduction to Functional Data Analysis provides a concise textbook introduction to the field. It explains how to analyze functional data, both at exploratory and inferential levels. It also provides a systematic and accessible exposition of the methodology and the required mathematical framework. The book can be used as textbook for a semester-long course on FDA for advanced undergraduate or MS statistics majors, as well as for MS and PhD students in other disciplines, including applied mathematics, environmental science, public health, medical research, geophysical sciences and economics. It can also be used for self-study and as a reference for researchers in those fields who wish to acquire solid understanding of FDA methodology and practical guidance for its implementation. Each chapter contains plentiful examples of relevant R code and theoretical and data analytic problems. The material of the book can be roughly divided into four parts of approximately equal length: 1) basic concepts and techniques of FDA, 2) functional regression models, 3) sparse and dependent functional data, and 4) introduction to the Hilbert space framework of FDA. The book assumes advanced undergraduate background in calculus, linear algebra, distributional probability theory, foundations of statistical inference, and some familiarity with R programming. Other required statistics background is provided in scalar settings before the related functional concepts are developed. Most chapters end with references to more advanced research for those who wish to gain a more in-depth understanding of a specific topic.

Author : Ciprian M. Crainiceanu,Jeff Goldsmith,Andrew Leroux,Erjia Cui
Publisher : CRC Press
Page : 338 pages
File Size : 51,7 Mb
Release : 2024-03-11
Category : Mathematics
ISBN : 9781003856306

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Functional Data Analysis with R by Ciprian M. Crainiceanu,Jeff Goldsmith,Andrew Leroux,Erjia Cui Pdf

Emerging technologies generate data sets of increased size and complexity that require new or updated statistical inferential methods and scalable, reproducible software. These data sets often involve measurements of a continuous underlying process, and benefit from a functional data perspective. Functional Data Analysis with R presents many ideas for handling functional data including dimension reduction techniques, smoothing, functional regression, structured decompositions of curves, and clustering. The idea is for the reader to be able to immediately reproduce the results in the book, implement these methods, and potentially design new methods and software that may be inspired by these approaches. Features: Functional regression models receive a modern treatment that allows extensions to many practical scenarios and development of state-of-the-art software. The connection between functional regression, penalized smoothing, and mixed effects models is used as the cornerstone for inference. Multilevel, longitudinal, and structured functional data are discussed with emphasis on emerging functional data structures. Methods for clustering functional data before and after smoothing are discussed. Multiple new functional data sets with dense and sparse sampling designs from various application areas are presented, including the NHANES linked accelerometry and mortality data, COVID-19 mortality data, CD4 counts data, and the CONTENT child growth study. Step-by-step software implementations are included, along with a supplementary website (www.FunctionalDataAnalysis.com) featuring software, data, and tutorials. More than 100 plots for visualization of functional data are presented. Functional Data Analysis with R is primarily aimed at undergraduate, master's, and PhD students, as well as data scientists and researchers working on functional data analysis. The book can be read at different levels and combines state-of-the-art software, methods, and inference. It can be used for self-learning, teaching, and research, and will particularly appeal to anyone who is interested in practical methods for hands-on, problem-forward functional data analysis. The reader should have some basic coding experience, but expertise in R is not required.

Author : Jin-Ting Zhang
Publisher : CRC Press
Page : 406 pages
File Size : 51,5 Mb
Release : 2013-06-18
Category : Mathematics
ISBN : 9781439862742

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Analysis of Variance for Functional Data by Jin-Ting Zhang Pdf

Despite research interest in functional data analysis in the last three decades, few books are available on the subject. Filling this gap, Analysis of Variance for Functional Data presents up-to-date hypothesis testing methods for functional data analysis. The book covers the reconstruction of functional observations, functional ANOVA, functional l

Author : Jorge Mateu,Ramon Giraldo
Publisher : John Wiley & Sons
Page : 452 pages
File Size : 46,5 Mb
Release : 2021-12-13
Category : Social Science
ISBN : 9781119387848

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Geostatistical Functional Data Analysis by Jorge Mateu,Ramon Giraldo Pdf

Geostatistical Functional Data Analysis Explore the intersection between geostatistics and functional data analysis with this insightful new reference Geostatistical Functional Data Analysis presents a unified approach to modelling functional data when spatial and spatio-temporal correlations are present. The Editors link together the wide research areas of geostatistics and functional data analysis to provide the reader with a new area called geostatistical functional data analysis that will bring new insights and new open questions to researchers coming from both scientific fields. This book provides a complete and up-to-date account to deal with functional data that is spatially correlated, but also includes the most innovative developments in different open avenues in this field. Containing contributions from leading experts in the field, this practical guide provides readers with the necessary tools to employ and adapt classic statistical techniques to handle spatial regression. The book also includes: A thorough introduction to the spatial kriging methodology when working with functions A detailed exposition of more classical statistical techniques adapted to the functional case and extended to handle spatial correlations Practical discussions of ANOVA, regression, and clustering methods to explore spatial correlation in a collection of curves sampled in a region In-depth explorations of the similarities and differences between spatio-temporal data analysis and functional data analysis Aimed at mathematicians, statisticians, postgraduate students, and researchers involved in the analysis of functional and spatial data, Geostatistical Functional Data Analysis will also prove to be a powerful addition to the libraries of geoscientists, environmental scientists, and economists seeking insightful new knowledge and questions at the interface of geostatistics and functional data analysis.

Author : Juš Kocijan
Publisher : Springer
Page : 267 pages
File Size : 45,5 Mb
Release : 2015-11-21
Category : Technology & Engineering
ISBN : 9783319210216

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Modelling and Control of Dynamic Systems Using Gaussian Process Models by Juš Kocijan Pdf

This monograph opens up new horizons for engineers and researchers in academia and in industry dealing with or interested in new developments in the field of system identification and control. It emphasizes guidelines for working solutions and practical advice for their implementation rather than the theoretical background of Gaussian process (GP) models. The book demonstrates the potential of this recent development in probabilistic machine-learning methods and gives the reader an intuitive understanding of the topic. The current state of the art is treated along with possible future directions for research. Systems control design relies on mathematical models and these may be developed from measurement data. This process of system identification, when based on GP models, can play an integral part of control design in data-based control and its description as such is an essential aspect of the text. The background of GP regression is introduced first with system identification and incorporation of prior knowledge then leading into full-blown control. The book is illustrated by extensive use of examples, line drawings, and graphical presentation of computer-simulation results and plant measurements. The research results presented are applied in real-life case studies drawn from successful applications including: a gas–liquid separator control; urban-traffic signal modelling and reconstruction; and prediction of atmospheric ozone concentration. A MATLAB® toolbox, for identification and simulation of dynamic GP models is provided for download.

Author : Robert B. Gramacy
Publisher : CRC Press
Page : 560 pages
File Size : 46,8 Mb
Release : 2020-03-10
Category : Mathematics
ISBN : 9781000766202

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Surrogates by Robert B. Gramacy Pdf

Computer simulation experiments are essential to modern scientific discovery, whether that be in physics, chemistry, biology, epidemiology, ecology, engineering, etc. Surrogates are meta-models of computer simulations, used to solve mathematical models that are too intricate to be worked by hand. Gaussian process (GP) regression is a supremely flexible tool for the analysis of computer simulation experiments. This book presents an applied introduction to GP regression for modelling and optimization of computer simulation experiments. Features: • Emphasis on methods, applications, and reproducibility. • R code is integrated throughout for application of the methods. • Includes more than 200 full colour figures. • Includes many exercises to supplement understanding, with separate solutions available from the author. • Supported by a website with full code available to reproduce all methods and examples. The book is primarily designed as a textbook for postgraduate students studying GP regression from mathematics, statistics, computer science, and engineering. Given the breadth of examples, it could also be used by researchers from these fields, as well as from economics, life science, social science, etc.

Author : Lajos Horváth,Piotr Kokoszka
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 54,6 Mb
Release : 2012-05-08
Category : Mathematics
ISBN : 9781461436553

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Inference for Functional Data with Applications by Lajos Horváth,Piotr Kokoszka Pdf

This book presents recently developed statistical methods and theory required for the application of the tools of functional data analysis to problems arising in geosciences, finance, economics and biology. It is concerned with inference based on second order statistics, especially those related to the functional principal component analysis. While it covers inference for independent and identically distributed functional data, its distinguishing feature is an in depth coverage of dependent functional data structures, including functional time series and spatially indexed functions. Specific inferential problems studied include two sample inference, change point analysis, tests for dependence in data and model residuals and functional prediction. All procedures are described algorithmically, illustrated on simulated and real data sets, and supported by a complete asymptotic theory. The book can be read at two levels. Readers interested primarily in methodology will find detailed descriptions of the methods and examples of their application. Researchers interested also in mathematical foundations will find carefully developed theory. The organization of the chapters makes it easy for the reader to choose an appropriate focus. The book introduces the requisite, and frequently used, Hilbert space formalism in a systematic manner. This will be useful to graduate or advanced undergraduate students seeking a self-contained introduction to the subject. Advanced researchers will find novel asymptotic arguments.

Author : James Ramsay,B. W. Silverman
Publisher : Springer Science & Business Media
Page : 464 pages
File Size : 46,5 Mb
Release : 2005-06-08
Category : Mathematics
ISBN : 038740080X

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Functional Data Analysis by James Ramsay,B. W. Silverman Pdf

This is the second edition of a highly succesful book which has sold nearly 3000 copies world wide since its publication in 1997. Many chapters will be rewritten and expanded due to a lot of progress in these areas since the publication of the first edition. Bernard Silverman is the author of two other books, each of which has lifetime sales of more than 4000 copies. He has a great reputation both as a researcher and an author. This is likely to be the bestselling book in the Springer Series in Statistics for a couple of years.

Author : D. M. Titterington,A. F. M. Smith,Adrian F. M. Smith,U. E. Makov
Publisher : Unknown
Page : 264 pages
File Size : 43,8 Mb
Release : 1985
Category : Mathematics
ISBN : UCSD:31822002319770

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Statistical Analysis of Finite Mixture Distributions by D. M. Titterington,A. F. M. Smith,Adrian F. M. Smith,U. E. Makov Pdf

In this book, the authors give a complete account of the applications, mathematical structure and statistical analysis of finite mixture distributions.

Author : Osval Antonio Montesinos López,Abelardo Montesinos López,José Crossa
Publisher : Springer Nature
Page : 707 pages
File Size : 47,7 Mb
Release : 2022-02-14
Category : Technology & Engineering
ISBN : 9783030890100

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Multivariate Statistical Machine Learning Methods for Genomic Prediction by Osval Antonio Montesinos López,Abelardo Montesinos López,José Crossa Pdf

This book is open access under a CC BY 4.0 license This open access book brings together the latest genome base prediction models currently being used by statisticians, breeders and data scientists. It provides an accessible way to understand the theory behind each statistical learning tool, the required pre-processing, the basics of model building, how to train statistical learning methods, the basic R scripts needed to implement each statistical learning tool, and the output of each tool. To do so, for each tool the book provides background theory, some elements of the R statistical software for its implementation, the conceptual underpinnings, and at least two illustrative examples with data from real-world genomic selection experiments. Lastly, worked-out examples help readers check their own comprehension.The book will greatly appeal to readers in plant (and animal) breeding, geneticists and statisticians, as it provides in a very accessible way the necessary theory, the appropriate R code, and illustrative examples for a complete understanding of each statistical learning tool. In addition, it weighs the advantages and disadvantages of each tool.

Author : Frédéric Ferraty,Philippe Vieu
Publisher : Springer Science & Business Media
Page : 260 pages
File Size : 47,5 Mb
Release : 2006-11-22
Category : Mathematics
ISBN : 9780387366203

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Nonparametric Functional Data Analysis by Frédéric Ferraty,Philippe Vieu Pdf

Modern apparatuses allow us to collect samples of functional data, mainly curves but also images. On the other hand, nonparametric statistics produces useful tools for standard data exploration. This book links these two fields of modern statistics by explaining how functional data can be studied through parameter-free statistical ideas. At the same time it shows how functional data can be studied through parameter-free statistical ideas, and offers an original presentation of new nonparametric statistical methods for functional data analysis.

Author : Nan Zhang
Publisher : Unknown
Page : 266 pages
File Size : 52,9 Mb
Release : 2006
Category : Electronic
ISBN : UCAL:X75961

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Functional Data Analysis for Non-Gaussian Longitudinal Data by Nan Zhang Pdf