Understanding Uncertainty

Deal with information and uncertainty properly and efficiently using tools emerging from generalized information theory Uncertainty and Information: Foundations of Generalized Information Theory contains comprehensive and up-to-date coverage of results that have emerged from a research program begun by the author in the early 1990s under the name «generalized information theory» (GIT). This ongoing research program aims to develop a formal mathematical treatment of the interrelated concepts of uncertainty and information in all their varieties. In GIT, as in classical information theory, uncertainty (predictive, retrodictive, diagnostic, prescriptive, and the like) is viewed as a manifestation of information deficiency, while information is viewed as anything capable of reducing the uncertainty. A broad conceptual framework for GIT is obtained by expanding the formalized language of classical set theory to include more expressive formalized languages based on fuzzy sets of various types, and by expanding classical theory of additive measures to include more expressive non-additive measures of various types. This landmark book examines each of several theories for dealing with particular types of uncertainty at the following four levels: * Mathematical formalization of the conceived type of uncertainty * Calculus for manipulating this particular type of uncertainty * Justifiable ways of measuring the amount of uncertainty in any situation formalizable in the theory * Methodological aspects of the theory With extensive use of examples and illustrations to clarify complex material and demonstrate practical applications, generous historical and bibliographical notes, end-of-chapter exercises to test readers' newfound knowledge, glossaries, and an Instructor's Manual, this is an excellent graduate-level textbook, as well as an outstanding reference for researchers and practitioners who deal with the various problems involving uncertainty and information. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

Science is a quest for certainty, but lack of certainty is the driving force behind all of its endeavors. This book, specifically, examines the uncertainty of technological and industrial science. Uncertainty and Mechanics studies the concepts of mechanical design in an uncertain setting and explains engineering techniques for inventing cost-effective products. Though it references practical applications, this is a book about ideas and potential advances in mechanical science.

Explores methods for the representation and treatment of uncertainty in risk assessment In providing guidance for practical decision-making situations concerning high-consequence technologies (e.g., nuclear, oil and gas, transport, etc.), the theories and methods studied in Uncertainty in Risk Assessment have wide-ranging applications from engineering and medicine to environmental impacts and natural disasters, security, and financial risk management. The main focus, however, is on engineering applications. While requiring some fundamental background in risk assessment, as well as a basic knowledge of probability theory and statistics, Uncertainty in Risk Assessment can be read profitably by a broad audience of professionals in the field, including researchers and graduate students on courses within risk analysis, statistics, engineering, and the physical sciences. Uncertainty in Risk Assessment: Illustrates the need for seeing beyond probability to represent uncertainties in risk assessment contexts. Provides simple explanations (supported by straightforward numerical examples) of the meaning of different types of probabilities, including interval probabilities, and the fundamentals of possibility theory and evidence theory. Offers guidance on when to use probability and when to use an alternative representation of uncertainty. Presents and discusses methods for the representation and characterization of uncertainty in risk assessment. Uses examples to clearly illustrate ideas and concepts.

Managing uncertainties in industrial systems is a daily challenge to ensure improved design, robust operation, accountable performance and responsive risk control. Authored by a leading European network of experts representing a cross section of industries, Uncertainty in Industrial Practice aims to provide a reference for the dissemination of uncertainty treatment in any type of industry. It is concerned with the quantification of uncertainties in the presence of data, model(s) and knowledge about the system, and offers a technical contribution to decision-making processes whilst acknowledging industrial constraints. The approach presented can be applied to a range of different business contexts, from research or early design through to certification or in-service processes. The authors aim to foster optimal trade-offs between literature-referenced methodologies and the simplified approaches often inevitable in practice, owing to data, time or budget limitations of technical decision-makers. Uncertainty in Industrial Practice: Features recent uncertainty case studies carried out in the nuclear, air & space, oil, mechanical and civil engineering industries set in a common methodological framework. Presents methods for organizing and treating uncertainties in a generic and prioritized perspective. Illustrates practical difficulties and solutions encountered according to the level of complexity, information available and regulatory and financial constraints. Discusses best practice in uncertainty modeling, propagation and sensitivity analysis through a variety of statistical and numerical methods. Reviews recent standards, references and available software, providing an essential resource for engineers and risk analysts in a wide variety of industries. This book provides a guide to dealing with quantitative uncertainty in engineering and modelling and is aimed at practitioners, including risk-industry regulators and academics wishing to develop industry-realistic methodologies.

Uncertainties are pervasive in natural hazards, and it is crucial to develop robust and meaningful approaches to characterize and communicate uncertainties to inform modeling efforts. In this monograph we provide a broad, cross-disciplinary overview of issues relating to uncertainties faced in natural hazard and risk assessment. We introduce some basic tenets of uncertainty analysis, discuss issues related to communication and decision support, and offer numerous examples of analyses and modeling approaches that vary by context and scope. Contributors include scientists from across the full breath of the natural hazard scientific community, from those in real-time analysis of natural hazards to those in the research community from academia and government. Key themes and highlights include: Substantial breadth and depth of analysis in terms of the types of natural hazards addressed, the disciplinary perspectives represented, and the number of studies included Targeted, application-centered analyses with a focus on development and use of modeling techniques to address various sources of uncertainty Emphasis on the impacts of climate change on natural hazard processes and outcomes Recommendations for cross-disciplinary and science transfer across natural hazard sciences This volume will be an excellent resource for those interested in the current work on uncertainty classification/quantification and will document common and emergent research themes to allow all to learn from each other and build a more connected but still diverse and ever growing community of scientists.

A valuable guide to understanding the problem of quantifying uncertainty in dose response relations for toxic substances In today's scientific research, there exists the need to address the topic of uncertainty as it pertains to dose response modeling. Uncertainty Modeling in Dose Response is the first book of its kind to implement and compare different methods for quantifying the uncertainty in the probability of response, as a function of dose. This volume gathers leading researchers in the field to properly address the issue while communicating concepts from diverse viewpoints and incorporating valuable insights. The result is a collection that reveals the properties, strengths, and weaknesses that exist in the various approaches to bench test problems. This book works with four bench test problems that were taken from real bioassay data for hazardous substances currently under study by the United States Environmental Protection Agency (EPA). The use of actual data provides readers with information that is relevant and representative of the current work being done in the field. Leading contributors from the toxicology and risk assessment communities have applied their methods to quantify model uncertainty in dose response for each case by employing various approaches, including Benchmark Dose Software methods, probabilistic inversion with isotonic regression, nonparametric Bayesian modeling, and Bayesian model averaging. Each chapter is reviewed and critiqued from three professional points of view: risk analyst/regulator, statistician/mathematician, and toxicologist/epidemiologist. In addition, all methodologies are worked out in detail, allowing readers to replicate these analyses and gain a thorough understanding of the methods. Uncertainty Modeling in Dose Response is an excellent book for courses on risk analysis and biostatistics at the upper-undergraduate and graduate levels. It also serves as a valuable reference for risk assessment, toxicology, biostatistics, and environmental chemistry professionals who wish to expand their knowledge and expertise in statistical dose response modeling problems and approaches.

Praise for the First Edition «. . . a readable, comprehensive volume that . . . belongs on the desk, close at hand, of any serious researcher or practitioner.» —Mathematical Geosciences The state of the art in geostatistics Geostatistical models and techniques such as kriging and stochastic multi-realizations exploit spatial correlations to evaluate natural resources, help optimize their development, and address environmental issues related to air and water quality, soil pollution, and forestry. Geostatistics: Modeling Spatial Uncertainty, Second Edition presents a comprehensive, up-to-date reference on the topic, now featuring the latest developments in the field. The authors explain both the theory and applications of geostatistics through a unified treatment that emphasizes methodology. Key topics that are the foundation of geostatistics are explored in-depth, including stationary and nonstationary models; linear and nonlinear methods; change of support; multivariate approaches; and conditional simulations. The Second Edition highlights the growing number of applications of geostatistical methods and discusses three key areas of growth in the field: New results and methods, including kriging very large datasets; kriging with outliers; nonse??parable space-time covariances; multipoint simulations; pluri-gaussian simulations; gradual deformation; and extreme value geostatistics Newly formed connections between geostatistics and other approaches such as radial basis functions, Gaussian Markov random fields, and data assimilation New perspectives on topics such as collocated cokriging, kriging with an external drift, discrete Gaussian change-of-support models, and simulation algorithms Geostatistics, Second Edition is an excellent book for courses on the topic at the graduate level. It also serves as an invaluable reference for earth scientists, mining and petroleum engineers, geophysicists, and environmental statisticians who collect and analyze data in their everyday work.

The first part of the book defines the concept of uncertainties and the mathematical frameworks that will be used for uncertainty modeling. The application to system reliability assessment illustrates the concept. In the second part, evidential networks as a new tool to model uncertainty in reliability and risk analysis is proposed and described. Then it is applied on SIS performance assessment and in risk analysis of a heat sink. In the third part, Bayesian and evidential networks are used to deal with important measures evaluation in the context of uncertainties.

Modeling Uncertainty in the Earth Sciences highlights the various issues, techniques and practical modeling tools available for modeling the uncertainty of complex Earth systems and the impact that it has on practical situations. The aim of the book is to provide an introductory overview which covers a broad range of tried-and-tested tools. Descriptions of concepts, philosophies, challenges, methodologies and workflows give the reader an understanding of the best way to make decisions under uncertainty for Earth Science problems. The book covers key issues such as: Spatial and time aspect; large complexity and dimensionality; computation power; costs of 'engineering' the Earth; uncertainty in the modeling and decision process. Focusing on reliable and practical methods this book provides an invaluable primer for the complex area of decision making with uncertainty in the Earth Sciences.

Extremism and the Psychology of Uncertainty showcases cutting-edge scientific research on the extent to which uncertainty may lead to extremism. Contributions come from leading international scholars who focus on a wide variety of forms, facets and manifestations of extremist behavior. Systematically integrates and explores the growing diversity of social psychological perspectives on the uncertainty extremism relationship Showcases contemporary cutting edge scientific research from leading international scholars Offers a broad perspective on extremism and focuses on a wide variety of different forms, facets and manifestations Accessible to social and behavioral scientists, policy makers and those with a genuine interest in understanding the psychology of extremism