Viatcheslav B. Melas – författare

The present book is devoted to studying optimal experimental designs for a wide class of linear and nonlinear regression models. This class includes polynomial, trigonometrical, rational, and exponential models as well as many particular models used in ecology and microbiology. As the criteria of optimality, the well known D-, E-, and c-criteria are implemented. The main idea of the book is to study the dependence of optimal - signs on values of unknown parameters and on the bounds of the design interval. Such a study can be performed on the base of the Implicit Fu- tion Theorem, the classical result of functional analysis. The idea was ?rst introduced in the author’s paper (Melas, 1978) for nonlinear in parameters exponential models. Recently, it was developed for other models in a n- ber of works (Melas (1995, 2000, 2001, 2004, 2005), Dette, Melas (2002, 2003), Dette, Melas, Pepelyshev (2002, 2003, 2004b), and Dette, Melas, Biederman (2002)). Thepurposeofthepresentbookistobringtogethertheresultsobtained and to develop further underlying concepts and tools. The approach, m- tioned above, will be called the functional approach. Its brief description can be found in the Introduction. The book contains eight chapters. The ?rst chapter introduces basic concepts and results of optimal design theory, initiated mainly by J.Kiefer.

The subject of the book is a functional theory of optimal designs elaborated by the author during the last two decades. This theory relates to points and weight of optimal designs considered as functions of some values. For linear models these values are metric characteristics of the set of admissible experimental conditions, for example, the bounds of a segment. For nonlinear models they are true values of the parameter to be estimated. Particularly locally D- optimal designs for exponential regression as an important example of nonlinear models and E-optimal designs for polynomial regression on arbitrary segments will be fully studied.

This text covers the experimental design theory called simulation experimental design, combining both the theory of experimental design and system simulation techniques. In particular, the mathematical theory of such universal variance reduction techniques as splitting and Russian Roulette is explored. The book contains a number of results on regression design theory related to nonlinear problems, the E-optimum criterion and designs which minimize bias. This volume should be useful to readers interested in systems simulation, applied statistics and numerical methods with basic knowledge of applied statistics and linear algebra.

This volume features original contributions and invited review articles on mathematical statistics, statistical simulation and experimental design. The selected peer-reviewed contributions originate from the 8th International Workshop on Simulation held in Vienna in 2015. The book is intended for mathematical statisticians, Ph.D. students and statisticians working in medicine, engineering, pharmacy, psychology, agriculture and other related fields.The International Workshops on Simulation are devoted to statistical techniques in stochastic simulation, data collection, design of scientific experiments and studies representing broad areas of interest. The first 6 workshops took place in St. Petersburg, Russia, in 1994 – 2009 and the 7th workshop was held in Rimini, Italy, in 2013.

This volume presents a selection of articles on statistical modeling and simulation, with a focus on different aspects of statistical estimation and testing problems, the design of experiments, reliability and queueing theory, inventory analysis, and the interplay between statistical inference, machine learning methods and related applications.

This volume presents a selection of articles on statistical modeling and simulation, with a focus on different aspects of statistical estimation and testing problems, the design of experiments, reliability and queueing theory, inventory analysis, and the interplay between statistical inference, machine learning methods and related applications. The refereed contributions originate from the 10th International Workshop on Simulation and Statistics, SimStat 2019, which was held in Salzburg, Austria, September 2–6, 2019, and were either presented at the conference or developed afterwards, relating closely to the topics of the workshop. The book is intended for statisticians and Ph.D. students who seek current developments and applications in the field.

This volume presents a selection of articles on statistical modeling and simulation, with a focus on different aspects of statistical estimation and testing problems, the design of experiments, reliability and queueing theory, inventory analysis, and the interplay between statistical inference, machine learning methods and related applications.

This volume features original contributions and invited review articles on mathematical statistics, statistical simulation and experimental design. The selected peer-reviewed contributions originate from the 8th International Workshop on Simulation held in Vienna in 2015. The book is intended for mathematical statisticians, Ph.D. students and statisticians working in medicine, engineering, pharmacy, psychology, agriculture and other related fields.The International Workshops on Simulation are devoted to statistical techniques in stochastic simulation, data collection, design of scientific experiments and studies representing broad areas of interest. The first 6 workshops took place in St. Petersburg, Russia, in 1994 – 2009 and the 7th workshop was held in Rimini, Italy, in 2013.