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 experim
This book describes methods for designing and analyzing experiments that are conducted using a computer code, a computer experiment, and, when possible, a physical experiment. Computer experiments continue to increase in popularity as surrogates for and adjuncts to physical experiments. Since the publication of the first edition, there have been many methodological advances and software developments to implement these new methodologies. The computer experiments literature has emphasized the construction of algorithms for various data analysis tasks (design construction, prediction, sensitivity analysis, calibration among others), and the development of web-based repositories of designs for immediate application. While it is written at a level that is accessible to readers with Masters-level training in Statistics, the book is written in sufficient detail to be useful for practitioners and researchers. New to this revised and expanded edition: • An expanded presentation of basic material on computer experiments and Gaussian processes with additional simulations and examples • A new comparison of plug-in prediction methodologies for real-valued simulator output • An enlarged discussion of space-filling designs including Latin Hypercube designs (LHDs), near-orthogonal designs, and nonrectangular regions • A chapter length description of process-based designs for optimization, to improve good overall fit, quantile estimation, and Pareto optimization • A new chapter describing graphical and numerical sensitivity analysis tools • Substantial new material on calibration-based prediction and inference for calibration parameters • Lists of software that can be used to fit models discussed in the book to aid practitioners
The use of computer modeling is fast increasing in almost every scientific, engineering and business arena. This dissertation investigates some challenging issues in design, modeling and analysis of computer experiments, which will consist of four major parts. In the first part, a new approach is developed to combine data from approximate and detailed simulations to build a surrogate model based on some stochastic models. In the second part, we propose some Bayesian hierarchical Gaussian process models to integrate data from different types of experiments. The third part concerns the development of latent variable models for computer experiments with multivariate response with application to data center temperature modeling. The last chapter is devoted to the development of nested space-filling designs for multiple experiments with different levels of accuracy.
This is a new edition of Kleijnen’s advanced expository book on statistical methods for the Design and Analysis of Simulation Experiments (DASE). Altogether, this new edition has approximately 50% new material not in the original book. More specifically, the author has made significant changes to the book’s organization, including placing the chapter on Screening Designs immediately after the chapters on Classic Designs, and reversing the order of the chapters on Simulation Optimization and Kriging Metamodels. The latter two chapters reflect how active the research has been in these areas. The validation section has been moved into the chapter on Classic Assumptions versus Simulation Practice, and the chapter on Screening now has a section on selecting the number of replications in sequential bifurcation through Wald’s sequential probability ration test, as well as a section on sequential bifurcation for multiple types of simulation responses. Whereas all references in the original edition were placed at the end of the book, in this edition references are placed at the end of each chapter. From Reviews of the First Edition: “Jack Kleijnen has once again produced a cutting-edge approach to the design and analysis of simulation experiments.” (William E. BILES, JASA, June 2009, Vol. 104, No. 486)
Here, the authors explain the basic ideas so as to generate interest in modern problems of experimental design. The topics discussed include designs for inference based on nonlinear models, designs for models with random parameters and stochastic processes, designs for model discrimination and incorrectly specified (contaminated) models, as well as examples of designs in functional spaces. Since the authors avoid technical details, the book assumes only a moderate background in calculus, matrix algebra, and statistics. However, at many places, hints are given as to how readers may enhance and adopt the basic ideas for advanced problems or applications. This allows the book to be used for courses at different levels, as well as serving as a useful reference for graduate students and researchers in statistics and engineering.
Many problems in science and engineering are solved through experimental investigations. Because experiments can be costly and time consuming, it is important to efficiently design the experiment so that maximum information about the problem can be obtained. It is also important to devise efficient statistical methods to analyze the experimental data so that none of the information is lost. This thesis makes contributions on several aspects in the field of design and analysis of experiments. It consists of two parts. The first part focuses on physical experiments, and the second part on computer experiments.
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.
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.
