Kai-Tai Fang - Böcker

Computer simulations based on mathematical models have become ubiquitous across the engineering disciplines and throughout the physical sciences. Successful use of a simulation model, however, requires careful interrogation of the model through systematic computer experiments. While specific theoretical/mathematical examinations of computer experiment design are available, those interested in applying proposed methodologies need a practical presentation and straightforward guidance on analyzing and interpreting experiment results.Written by authors with strong academic reputations and real-world practical experience, Design and Modeling for Computer Experiments is exactly the kind of treatment you need. The authors blend a sound, modern statistical approach with extensive engineering applications and clearly delineate the steps required to successfully model a problem and provide an analysis that will help find the solution. Part I introduces the design and modeling of computer experiments and the basic concepts used throughout the book. Part II focuses on the design of computer experiments. The authors present the most popular space-filling designs - like Latin hypercube sampling and its modifications and uniform design - including their definitions, properties, construction and related generating algorithms. Part III discusses the modeling of data from computer experiments. Here the authors present various modeling techniques and discuss model interpretation, including sensitivity analysis. An appendix reviews the statistics and mathematics concepts needed, and numerous examples clarify the techniques and their implementation.The complexity of real physical systems means that there is usually no simple analytic formula that sufficiently describes the phenomena. Useful both as a textbook and professional reference, this book presents the techniques you need to design and model computer experiments for practical problem solving.

Growth-curve models are generalized multivariate analysis-of-variance models. These models are especially useful for investigating growth problems on short times in economics, biology, medical research, and epidemiology. This book systematically introduces the theory of the GCM with particular emphasis on their multivariate statistical diagnostics, which are based mainly on recent developments made by the authors and their collaborators. The authors provide complete proofs of theorems as well as practical data sets and MATLAB code.

Statistical simulation has become a cornerstone in statistical research and applications. The aim of Representative Points of Statistical Distributions: Applications in Statistical Inference is to present a comprehensive exploration of various methods for statistical simulation and resampling, focusing on consistency and efficiency. It covers a range of representative points (RPs) – Monte Carlo (MC) RPs, quasi-Monte Carlo (QMC) RPs, and mean square error (MSE) RPs – and their applications, and includes a collection of recent developments in the field. It also explores other types of representative points and the corresponding approximate distributions, and delves into the realm of statistical simulation by exploring the limitations of traditional MC methods and the innovations brought about by the bootstrap method. In addition, the text introduces other kinds of representative points and the corresponding approximate distributions such as QMC and MSE methods.FeaturesComprehensive exploration of statistical simulation methods: provides a deep dive into MC methods and bootstrap methods, and introduces other kinds of RPs and the corresponding approximate distributions, such as QMC and MSE methods.Emphasis on consistency and efficiency: highlights the advantages of these methods in terms of consistency and efficiency, addressing the slow convergence rate of classical statistical simulation.Collection of recent developments: brings together the latest advancements in the field of statistical simulation, keeping readers up to date with the most current research.Practical applications: includes numerous practical applications of various types of RPs (MC-RPs, QMC-RPs, and MSE-RPs) in statistical inference and simulation.Educational resource: can serve as a textbook for postgraduate students, a reference book for undergraduate students, and a valuable resource for professionals in various fields.The book serves as a valuable resource for postgraduate students, researchers, and practitioners in statistics, mathematics, and other quantitative fields.

Since the publication of the by now classical Johnson and Kotz Continuous Multivariate Distributions (Wiley, 1972) there have been substantial developments in multivariate distribution theory especially in the area of non-normal symmetric multivariate distributions. The book by Fang, Kotz and Ng summarizes these developments in a manner which is accessible to a reader with only limited background (advanced real-analysis calculus, linear algebra and elementary matrix calculus). Many of the results in this field are due to Kai-Tai Fang and his associates and appeared in Chinese publications only.A thorough literature search was conducted and the book represents the latest work - as of 1988 - in this rapidly developing field of multivariate distributions. The authors are experts in statistical distribution theory.

Growth-curve models are generalized multivariate analysis-of-variance models. These models are especially useful for investigating growth problems on short times in economics, biology, medical research, and epidemiology. This book systematically introduces the theory of the GCM with particular emphasis on their multivariate statistical diagnostics, which are based mainly on recent developments made by the authors and their collaborators. The authors provide complete proofs of theorems as well as practical data sets and MATLAB code.

Computer simulations based on mathematical models have become ubiquitous across the engineering disciplines and throughout the physical sciences. Successful use of a simulation model, however, requires careful interrogation of the model through systematic computer experiments. While specific theoretical/mathematical examinations of computer experiment design are available, those interested in applying proposed methodologies need a practical presentation and straightforward guidance on analyzing and interpreting experiment results.Written by authors with strong academic reputations and real-world practical experience, Design and Modeling for Computer Experiments is exactly the kind of treatment you need. The authors blend a sound, modern statistical approach with extensive engineering applications and clearly delineate the steps required to successfully model a problem and provide an analysis that will help find the solution. Part I introduces the design and modeling of computer experiments and the basic concepts used throughout the book. Part II focuses on the design of computer experiments. The authors present the most popular space-filling designs - like Latin hypercube sampling and its modifications and uniform design - including their definitions, properties, construction and related generating algorithms. Part III discusses the modeling of data from computer experiments. Here the authors present various modeling techniques and discuss model interpretation, including sensitivity analysis. An appendix reviews the statistics and mathematics concepts needed, and numerous examples clarify the techniques and their implementation.The complexity of real physical systems means that there is usually no simple analytic formula that sufficiently describes the phenomena. Useful both as a textbook and professional reference, this book presents the techniques you need to design and model computer experiments for practical problem solving.

This volume represents the refereed proceedings of the Fourth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2000) which was held at Hong Kong Baptist Uni- versity from November 27 to December 1, 2000. The program of this con- ference was arranged by a committee consisting of Kurt Binder (Univer- sitat Mainz), Kai-Tai Fang (Hong Kong Baptist University, co-chair), Rus- sel Caflisch (University of California at Los Angeles), George S. Fishman (University of North Carolina), Masanori Fushimi (Nanzan University), Paul Glasserman (Columbia University), Fred J. Hickernell (Hong Kong Baptist University), Pierre L'Ecuyer (Universite de Montreal), Harald Niederreiter (National University of Singapore, co-chair), Art B. Owen (Stanford Univer- sity), Ian H. Sloan (University of New South Wales), Jerome Spanier (Clare- mont Graduate University), Yuan Wang (Chinese Academy of Sciences), and Henryk Wozniakowski (Columbia University and University of Warsaw).The local arrangements were in the hands of an organizing committee compris- ing Wai-Yan Cheng (City University of Hong Kong), Kai-Tai Fang (Hong Kong Baptist University, co-chair), Minggao Gu (Chinese University of Hong Kong), Fred J. Hickernell (Hong Kong Baptist University, co-chair) , Irwin King (Chinese University of Hong Kong), Yue-Kuen Kwok (Hong Kong Uni- versity of Science and Technology), Li-Zhi Liao (Hong Kong Baptist Univer- sity), and Lei-Han Tang (Hong Kong Baptist University).