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Author : Marian Farah
Publisher :
Page : 296 pages
File Size : 40,12 MB
Release : 2011
Category :
ISBN :
Author : Robert B. Gramacy
Publisher : CRC Press
Page : 560 pages
File Size : 48,96 MB
Release : 2020-03-10
Category : Mathematics
ISBN : 1000766209
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.
Author : Chenguang Wang
Publisher :
Page : pages
File Size : 25,26 MB
Release : 2010
Category :
ISBN :
In Chapter 4, we discuss pattern mixture models. Pattern mixture modeling is a popular approach for handling incomplete longitudinal data. Such models are not identifiable by construction. Identifying restrictions are one approach to mixture model identification (Daniels and Hogan, 2008; Kenward et al., 2003; Little, 1995; Little and Wang, 1996; Thijs et al., 2002) and are a natural starting point for missing not at random sensitivity analysis (Daniels and Hogan, 2008; Thijs et al., 2002). However, when the pattern specific models are multivariate normal (MVN), identifying restrictions corresponding to missing at random may not exist. Furthermore, identification strategies can be problematic in models with covariates (e.g. baseline covariates with time-invariant coefficients). In this paper, we explore conditions necessary for identifying restrictions that result in missing at random (MAR) to exist under a multivariate normality assumption and strategies for identifying sensitivity parameters for sensitivity analysis or for a fully Bayesian analysis with informative priors. A longitudinal clinical trial is used for illustration of sensitivity analysis. Problems caused by baseline covariates with time-invariant coefficients are investigated and an alternative identifying restriction based on residuals is proposed as a solution.
Author : Thomas J. Santner
Publisher : Springer
Page : 436 pages
File Size : 30,93 MB
Release : 2019-01-08
Category : Mathematics
ISBN : 1493988476
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
Author : Andrea Saltelli
Publisher : John Wiley & Sons
Page : 304 pages
File Size : 29,77 MB
Release : 2008-02-28
Category : Mathematics
ISBN : 9780470725177
Complex mathematical and computational models are used in all areas of society and technology and yet model based science is increasingly contested or refuted, especially when models are applied to controversial themes in domains such as health, the environment or the economy. More stringent standards of proofs are demanded from model-based numbers, especially when these numbers represent potential financial losses, threats to human health or the state of the environment. Quantitative sensitivity analysis is generally agreed to be one such standard. Mathematical models are good at mapping assumptions into inferences. A modeller makes assumptions about laws pertaining to the system, about its status and a plethora of other, often arcane, system variables and internal model settings. To what extent can we rely on the model-based inference when most of these assumptions are fraught with uncertainties? Global Sensitivity Analysis offers an accessible treatment of such problems via quantitative sensitivity analysis, beginning with the first principles and guiding the reader through the full range of recommended practices with a rich set of solved exercises. The text explains the motivation for sensitivity analysis, reviews the required statistical concepts, and provides a guide to potential applications. The book: Provides a self-contained treatment of the subject, allowing readers to learn and practice global sensitivity analysis without further materials. Presents ways to frame the analysis, interpret its results, and avoid potential pitfalls. Features numerous exercises and solved problems to help illustrate the applications. Is authored by leading sensitivity analysis practitioners, combining a range of disciplinary backgrounds. Postgraduate students and practitioners in a wide range of subjects, including statistics, mathematics, engineering, physics, chemistry, environmental sciences, biology, toxicology, actuarial sciences, and econometrics will find much of use here. This book will prove equally valuable to engineers working on risk analysis and to financial analysts concerned with pricing and hedging.
Author : Roger Ghanem
Publisher : Springer
Page : 0 pages
File Size : 10,82 MB
Release : 2016-05-08
Category : Mathematics
ISBN : 9783319123844
The topic of Uncertainty Quantification (UQ) has witnessed massive developments in response to the promise of achieving risk mitigation through scientific prediction. It has led to the integration of ideas from mathematics, statistics and engineering being used to lend credence to predictive assessments of risk but also to design actions (by engineers, scientists and investors) that are consistent with risk aversion. The objective of this Handbook is to facilitate the dissemination of the forefront of UQ ideas to their audiences. We recognize that these audiences are varied, with interests ranging from theory to application, and from research to development and even execution.
Author : National Research Council
Publisher : National Academies Press
Page : 152 pages
File Size : 40,50 MB
Release : 2008-10-24
Category : Technology & Engineering
ISBN : 0309119995
Integrated computational materials engineering (ICME) is an emerging discipline that can accelerate materials development and unify design and manufacturing. Developing ICME is a grand challenge that could provide significant economic benefit. To help develop a strategy for development of this new technology area, DOE and DoD asked the NRC to explore its benefits and promises, including the benefits of a comprehensive ICME capability; to establish a strategy for development and maintenance of an ICME infrastructure, and to make recommendations about how best to meet these opportunities. This book provides a vision for ICME, a review of case studies and lessons learned, an analysis of technological barriers, and an evaluation of ways to overcome cultural and organizational challenges to develop the discipline.
Author : Jun S. Liu
Publisher : Springer Science & Business Media
Page : 350 pages
File Size : 35,55 MB
Release : 2013-11-11
Category : Mathematics
ISBN : 0387763716
This book provides a self-contained and up-to-date treatment of the Monte Carlo method and develops a common framework under which various Monte Carlo techniques can be "standardized" and compared. Given the interdisciplinary nature of the topics and a moderate prerequisite for the reader, this book should be of interest to a broad audience of quantitative researchers such as computational biologists, computer scientists, econometricians, engineers, probabilists, and statisticians. It can also be used as a textbook for a graduate-level course on Monte Carlo methods.
Author : Shane G. Henderson
Publisher : Elsevier
Page : 693 pages
File Size : 25,67 MB
Release : 2006-09-02
Category : Business & Economics
ISBN : 0080464769
This Handbook is a collection of chapters on key issues in the design and analysis of computer simulation experiments on models of stochastic systems. The chapters are tightly focused and written by experts in each area. For the purpose of this volume “simulation refers to the analysis of stochastic processes through the generation of sample paths (realization) of the processes. Attention focuses on design and analysis issues and the goal of this volume is to survey the concepts, principles, tools and techniques that underlie the theory and practice of stochastic simulation design and analysis. Emphasis is placed on the ideas and methods that are likely to remain an intrinsic part of the foundation of the field for the foreseeable future. The chapters provide up-to-date references for both the simulation researcher and the advanced simulation user, but they do not constitute an introductory level ‘how to’ guide. Computer scientists, financial analysts, industrial engineers, management scientists, operations researchers and many other professionals use stochastic simulation to design, understand and improve communications, financial, manufacturing, logistics, and service systems. A theme that runs throughout these diverse applications is the need to evaluate system performance in the face of uncertainty, including uncertainty in user load, interest rates, demand for product, availability of goods, cost of transportation and equipment failures. * Tightly focused chapters written by experts* Surveys concepts, principles, tools, and techniques that underlie the theory and practice of stochastic simulation design and analysis* Provides an up-to-date reference for both simulation researchers and advanced simulation users
Author : Peter Diggle
Publisher : Springer Science & Business Media
Page : 242 pages
File Size : 15,96 MB
Release : 2007-05-26
Category : Science
ISBN : 0387485368
This volume is the first book-length treatment of model-based geostatistics. The text is expository, emphasizing statistical methods and applications rather than the underlying mathematical theory. Analyses of datasets from a range of scientific contexts feature prominently, and simulations are used to illustrate theoretical results. Readers can reproduce most of the computational results in the book by using the authors' software package, geoR, whose usage is illustrated in a computation section at the end of each chapter. The book assumes a working knowledge of classical and Bayesian methods of inference, linear models, and generalized linear models.