Thomas J. Santner

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 Statistical Analysis of Discrete Data provides an introduction to cur­ rent statistical methods for analyzing discrete response data. The book can be used as a course text for graduate students and as a reference for researchers who analyze discrete data. The book's mathematical prereq­ uisites are linear algebra and elementary advanced calculus. It assumes a basic statistics course which includes some decision theory, and knowledge of classical linear model theory for continuous response data. Problems are provided at the end of each chapter to give the reader an opportunity to ap­ ply the methods in the text, to explore extensions of the material covered, and to analyze data with discrete responses. In the text examples, and in the problems, we have sought to include interesting data sets from a wide variety of fields including political science, medicine, nuclear engineering, sociology, ecology, cancer research, library science, and biology. Although there are several texts available on discrete data analysis, we felt there was a need for a book which incorporated some of the myriad recent research advances. Our motivation was to introduce the subject by emphasizing its ties to the well-known theories of linear models, experi­ mental design, and regression diagnostics, as well as to describe alterna­ tive methodologies (Bayesian, smoothing, etc. ); the latter are based on the premise that external information is available. These overriding goals, to­ gether with our own experiences and biases, have governed our choice of topics.

In the past 15 to 20 years, the computer has become a popular tool for exploring the relationship between a measured response and factors thought to affect the response. In many cases, scientific theories exist that implicitly relate the response to the factors by means of systems of mathematical equations. There also exist numerical methods for accurately solving such equations and appropriate computer hardware and software to implement these methods. In many engineering applications, for example, the relationship is described by a dynamical system and the numerical method is a finite element code. In such situations, these numerical methods allow one to produce computer code that can generate the response corresponding to any given set of values of the factors. This allows one to conduct an "experiment" (called a "computer experiment") to explore the relationship between the response and the factors using the code. Indeed, in some cases computer experimentation is feasible when a properly designed physical experiment (the gold standard for establishing cause and effect) is impossible. For example, the number of input variables may be too large to consider performing a physical experiment or it may simply be economically prohibitive to run an experiment on the scale required to gather sufficient information to answer a particular research question. This book describes methods for designing and analyzing experiments conducted using computer code in lieu of a physical experiment. It discusses how to select the values of the factors at which to run the code (the design of the computer experiment) in light of the research objectives of the experimenter. It also provides techniques for analyzing the resulting data so as to achieve these research goals.

A practical guide to selection, screening, and multiple comparisonsThis book addresses experimenters who have knowledge of classical experimental design methodology and expands their repertoire beyond hypothesis testing by providing statistical methods appropriate for selection, screening, and multiple comparisons. It concentrates on three types of procedures: selection procedures that use the "indifference-zone" approach, screening procedures using the "subset" approach, and multiple comparison procedures involving normal means. This is the first book, specifically designed for practitioners, to bring into focus many developments in the field previously covered only in university courses. It also presents new results on the comparison of procedures that have been obtained specifically for this volume. This self-contained volume describes methods for designing experiments when the scientific objective is selection of best treatments, screening a set of treatments, and multiple comparisons among treatment means. The book emphasizes procedures appropriate in a variety of practical settings including those that require blocking and randomization restriction. It compares the relative merits of procedures when several different methods can be used in the same circumstances. Providing practical guidance for experimenters in agriculture, engineering, medicine, and other empirical sciences, this book may also be used for a one-semester graduate course in selection methodology or to augment traditional courses in experimental design. Design and Analysis of Experiments for Statistical Selection, Screening, and Multiple Comparisons: *Shows how selection and screening can be applied to data that follow one of three important probability models—normal distribution, binomial distribution, and the multinomial distribution models *Provides an extensive comparison of procedures, allowing experimenters to choose among competitors when several different procedures are feasible for a given application *Gives an extensive set of tables of constants necessary to implement the procedures *Supplements the tables of constants with listings of FORTRAN programs so that experimenters are not limited to those values covered by the tables *Focuses on frequent formulations, while also providing references to Bayesian and other alternative developments in the Chapter Notes

The Statistical Analysis of Discrete Data provides an introduction to cur­ rent statistical methods for analyzing discrete response data. The book can be used as a course text for graduate students and as a reference for researchers who analyze discrete data. The book's mathematical prereq­ uisites are linear algebra and elementary advanced calculus. It assumes a basic statistics course which includes some decision theory, and knowledge of classical linear model theory for continuous response data. Problems are provided at the end of each chapter to give the reader an opportunity to ap­ ply the methods in the text, to explore extensions of the material covered, and to analyze data with discrete responses. In the text examples, and in the problems, we have sought to include interesting data sets from a wide variety of fields including political science, medicine, nuclear engineering, sociology, ecology, cancer research, library science, and biology. Although there are several texts available on discrete data analysis, we felt there was a need for a book which incorporated some of the myriad recent research advances. Our motivation was to introduce the subject by emphasizing its ties to the well-known theories of linear models, experi­ mental design, and regression diagnostics, as well as to describe alterna­ tive methodologies (Bayesian, smoothing, etc. ); the latter are based on the premise that external information is available. These overriding goals, to­ gether with our own experiences and biases, have governed our choice of topics.