Bayesian Treed Gaussian Process Models
Author : Robert B. Gramacy
Publisher :
Page : 330 pages
File Size : 29,61 MB
Release : 2005
Category :
ISBN :
Author : Robert B. Gramacy
Publisher :
Page : 330 pages
File Size : 29,61 MB
Release : 2005
Category :
ISBN :
Author : Robert B. Gramacy
Publisher : CRC Press
Page : 560 pages
File Size : 27,92 MB
Release : 2020-03-10
Category : Mathematics
ISBN : 1000766209
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 : Anthony O' Hagan
Publisher : OUP Oxford
Page : 924 pages
File Size : 46,81 MB
Release : 2010-03-18
Category : Mathematics
ISBN : 0191613894
Bayesian analysis has developed rapidly in applications in the last two decades and research in Bayesian methods remains dynamic and fast-growing. Dramatic advances in modelling concepts and computational technologies now enable routine application of Bayesian analysis using increasingly realistic stochastic models, and this drives the adoption of Bayesian approaches in many areas of science, technology, commerce, and industry. This Handbook explores contemporary Bayesian analysis across a variety of application areas. Chapters written by leading exponents of applied Bayesian analysis showcase the scientific ease and natural application of Bayesian modelling, and present solutions to real, engaging, societally important and demanding problems. The chapters are grouped into five general areas: Biomedical & Health Sciences; Industry, Economics & Finance; Environment & Ecology; Policy, Political & Social Sciences; and Natural & Engineering Sciences, and Appendix material in each touches on key concepts, models, and techniques of the chapter that are also of broader pedagogic and applied interest.
Author : José M. Bernardo
Publisher : Oxford University Press
Page : 717 pages
File Size : 19,88 MB
Release : 2011-10-06
Category : Mathematics
ISBN : 0199694583
Bayesian statistics is a dynamic and fast-growing area of statistical research and the Valencia International Meetings provide the main forum for discussion. These resulting proceedings form an up-to-date collection of research.
Author : Paul Damien
Publisher : OUP Oxford
Page : 717 pages
File Size : 28,28 MB
Release : 2013-01-24
Category : Mathematics
ISBN : 0191647004
The development of hierarchical models and Markov chain Monte Carlo (MCMC) techniques forms one of the most profound advances in Bayesian analysis since the 1970s and provides the basis for advances in virtually all areas of applied and theoretical Bayesian statistics. This volume guides the reader along a statistical journey that begins with the basic structure of Bayesian theory, and then provides details on most of the past and present advances in this field. The book has a unique format. There is an explanatory chapter devoted to each conceptual advance followed by journal-style chapters that provide applications or further advances on the concept. Thus, the volume is both a textbook and a compendium of papers covering a vast range of topics. It is appropriate for a well-informed novice interested in understanding the basic approach, methods and recent applications. Because of its advanced chapters and recent work, it is also appropriate for a more mature reader interested in recent applications and developments, and who may be looking for ideas that could spawn new research. Hence, the audience for this unique book would likely include academicians/practitioners, and could likely be required reading for undergraduate and graduate students in statistics, medicine, engineering, scientific computation, business, psychology, bio-informatics, computational physics, graphical models, neural networks, geosciences, and public policy. The book honours the contributions of Sir Adrian F. M. Smith, one of the seminal Bayesian researchers, with his papers on hierarchical models, sequential Monte Carlo, and Markov chain Monte Carlo and his mentoring of numerous graduate students -the chapters are authored by prominent statisticians influenced by him. Bayesian Theory and Applications should serve the dual purpose of a reference book, and a textbook in Bayesian Statistics.
Author : Slawomir Koziel
Publisher : Springer Science & Business Media
Page : 413 pages
File Size : 11,34 MB
Release : 2013-06-06
Category : Mathematics
ISBN : 1461475511
Contemporary engineering design is heavily based on computer simulations. Accurate, high-fidelity simulations are used not only for design verification but, even more importantly, to adjust parameters of the system to have it meet given performance requirements. Unfortunately, accurate simulations are often computationally very expensive with evaluation times as long as hours or even days per design, making design automation using conventional methods impractical. These and other problems can be alleviated by the development and employment of so-called surrogates that reliably represent the expensive, simulation-based model of the system or device of interest but they are much more reasonable and analytically tractable. This volume features surrogate-based modeling and optimization techniques, and their applications for solving difficult and computationally expensive engineering design problems. It begins by presenting the basic concepts and formulations of the surrogate-based modeling and optimization paradigm and then discusses relevant modeling techniques, optimization algorithms and design procedures, as well as state-of-the-art developments. The chapters are self-contained with basic concepts and formulations along with applications and examples. The book will be useful to researchers in engineering and mathematics, in particular those who employ computationally heavy simulations in their design work.
Author : Carl Edward Rasmussen
Publisher : MIT Press
Page : 266 pages
File Size : 47,68 MB
Release : 2005-11-23
Category : Computers
ISBN : 026218253X
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 : Nils Lid Hjort
Publisher : Cambridge University Press
Page : 309 pages
File Size : 23,72 MB
Release : 2010-04-12
Category : Mathematics
ISBN : 1139484605
Bayesian nonparametrics works - theoretically, computationally. The theory provides highly flexible models whose complexity grows appropriately with the amount of data. Computational issues, though challenging, are no longer intractable. All that is needed is an entry point: this intelligent book is the perfect guide to what can seem a forbidding landscape. Tutorial chapters by Ghosal, Lijoi and Prünster, Teh and Jordan, and Dunson advance from theory, to basic models and hierarchical modeling, to applications and implementation, particularly in computer science and biostatistics. These are complemented by companion chapters by the editors and Griffin and Quintana, providing additional models, examining computational issues, identifying future growth areas, and giving links to related topics. This coherent text gives ready access both to underlying principles and to state-of-the-art practice. Specific examples are drawn from information retrieval, NLP, machine vision, computational biology, biostatistics, and bioinformatics.
Author : Klaus Hinkelmann
Publisher : John Wiley & Sons
Page : 598 pages
File Size : 48,74 MB
Release : 2012-02-14
Category : Mathematics
ISBN : 0470530685
Provides timely applications, modifications, and extensions of experimental designs for a variety of disciplines Design and Analysis of Experiments, Volume 3: Special Designs and Applications continues building upon the philosophical foundations of experimental design by providing important, modern applications of experimental design to the many fields that utilize them. The book also presents optimal and efficient designs for practice and covers key topics in current statistical research. Featuring contributions from leading researchers and academics, the book demonstrates how the presented concepts are used across various fields from genetics and medicinal and pharmaceutical research to manufacturing, engineering, and national security. Each chapter includes an introduction followed by the historical background as well as in-depth procedures that aid in the construction and analysis of the discussed designs. Topical coverage includes: Genetic cross experiments, microarray experiments, and variety trials Clinical trials, group-sequential designs, and adaptive designs Fractional factorial and search, choice, and optimal designs for generalized linear models Computer experiments with applications to homeland security Robust parameter designs and split-plot type response surface designs Analysis of directional data experiments Throughout the book, illustrative and numerical examples utilize SAS®, JMP®, and R software programs to demonstrate the discussed techniques. Related data sets and software applications are available on the book's related FTP site. Design and Analysis of Experiments, Volume 3 is an ideal textbook for graduate courses in experimental design and also serves as a practical, hands-on reference for statisticians and researchers across a wide array of subject areas, including biological sciences, engineering, medicine, and business.
Author : Hermann Locarek-Junge
Publisher : Springer Science & Business Media
Page : 825 pages
File Size : 40,65 MB
Release : 2010-08-03
Category : Mathematics
ISBN : 3642107451
Clustering and Classification, Data Analysis, Data Handling and Business Intelligence are research areas at the intersection of statistics, mathematics, computer science and artificial intelligence. They cover general methods and techniques that can be applied to a vast set of applications such as in business and economics, marketing and finance, engineering, linguistics, archaeology, musicology, biology and medical science. This volume contains the revised versions of selected papers presented during the 11th Biennial IFCS Conference and 33rd Annual Conference of the German Classification Society (Gesellschaft für Klassifikation - GfKl). The conference was organized in cooperation with the International Federation of Classification Societies (IFCS), and was hosted by Dresden University of Technology, Germany, in March 2009.