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.

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 thereis 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.

The book provides necessary knowledge for readers interested in developing the theory of uniform experimental design. It discusses measures of uniformity, various construction methods of uniform designs, modeling techniques, design and modeling for experiments with mixtures, and the usefulness of the uniformity in block, factorial and supersaturated designs. Experimental design is an important branch of statistics with a long history, and is extremely useful in multi-factor experiments. Involving rich methodologies and various designs, it has played a key role in industry, technology, sciences and various other fields. A design that chooses experimental points uniformly scattered on the domain is known as uniform experimental design, and uniform experimental design can be regarded as a fractional factorial design with model uncertainty, a space-filling design for computer experiments, a robust design against the model specification, and a supersaturated design and can be applied to experiments with mixtures.

Growth-curve models are generalized multivariate analysis-of-variance models. The basic idea of the models is to use different polynomials to fit different treatment groups involved in the longitudinal study. It is not uncommon, however, to find outliers and influential observations in growth data that heavily affect statistical inference in growth curve models. This book provides a comprehensive introduction to the theory of growth curve models with an emphasis on statistical diagnostics. A variety of issues on model fittings and model diagnostics are addressed, and many criteria for outlier detection and influential observation identification are created within likelihood and Bayesian frameworks. This book is intended for postgraduates and statisticians whose research involves longitudinal study, multivariate analysis and statistical diagnostics, and also for scientists who analyze longitudinal data and repeated measures. The authors provide theoretical details on the model fittings and also emphasize the application of growth curve models to practical data analysis, which are reflected in the analysis of practical examples given in each chapter. The book assumes a basic knowledge of matrix algebra and linear regression. Jian-Xin Pan is a lecturer in Medical Statistics of Keele University in the U.K. He has published more than twenty papers on growth curve models, statistical diagnostics and linear/non-linear mixed models. He has a long-standing research interest in longitudinal data analysis and repeated measures in medicine and agriculture. Kai-Tai Fang is a chair professor in Statistics of Hong Kong Baptist University and a fellow of the Institute of Mathematical Statistics. He has published several books with Springer-Verlag, Chapman & Hall, and Science Press and is an author or co-author of over one hundred papers. His research interest includes generalized multivariate analysis, elliptically contoured distributions and uniform design.

Growth-curve models are generalized multivariate analysis-of-variance models. The basic idea of the models is to use different polynomials to fit different treatment groups involved in the longitudinal study. It is not uncommon, however, to find outliers and influential observations in growth data that heavily affect statistical inference in growth curve models. This book provides a comprehensive introduction to the theory of growth curve models with an emphasis on statistical diagnostics. A variety of issues on model fittings and model diagnostics are addressed, and many criteria for outlier detection and influential observation identification are created within likelihood and Bayesian frameworks. This book is intended for postgraduates and statisticians whose research involves longitudinal study, multivariate analysis and statistical diagnostics, and also for scientists who analyze longitudinal data and repeated measures. The authors provide theoretical details on the model fittings and also emphasize the application of growth curve models to practical data analysis, which are reflected in the analysis of practical examples given in each chapter. The book assumes a basic knowledge of matrix algebra and linear regression. Jian-Xin Pan is a lecturer in Medical Statistics of Keele University in the U.K. He has published more than twenty papers on growth curve models, statistical diagnostics and linear/non-linear mixed models. He has a long-standing research interest in longitudinal data analysis and repeated measures in medicine and agriculture. Kai-Tai Fang is a chair professor in Statistics of Hong Kong Baptist University and a fellow of the Institute of Mathematical Statistics. He has published several books with Springer-Verlag, Chapman & Hall, and Science Press and is an author or co-author of over one hundred papers. His research interest includes generalized multivariate analysis, elliptically contoured distributions and uniform design.

This book represents the refereed proceedings of the Fourth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing which was held at Hong Kong Baptist University in 2000. An important feature are invited surveys of the state-of-the-art in key areas such as multidimensional numerical integration, low-discrepancy point sets, random number generation, and applications of Monte Carlo and quasi-Monte Carlo methods. These proceedings include also carefully selected contributed papers on all aspects of Monte Carlo and quasi-Monte Carlo methods. The reader will be informed about current research in this very active field.