The world we live in is pervaded with uncertainty and imprecision. Is it likely to rain this afternoon? Should I take an umbrella with me? Will I be able to find parking near the campus? Should I go by bus? Such simple questions are a c- mon occurrence in our daily lives. Less simple examples: What is the probability that the price of oil will rise sharply in the near future? Should I buy Chevron stock? What are the chances that a bailout of GM, Ford and Chrysler will not s- ceed? What will be the consequences? Note that the examples in question involve both uncertainty and imprecision. In the real world, this is the norm rather than exception. There is a deep-seated tradition in science of employing probability theory, and only probability theory, to deal with uncertainty and imprecision. The mon- oly of probability theory came to an end when fuzzy logic made its debut. H- ever, this is by no means a widely accepted view. The belief persists, especially within the probability community, that probability theory is all that is needed to deal with uncertainty. To quote a prominent Bayesian, Professor Dennis Lindley, “The only satisfactory description of uncertainty is probability.

Modeling Uncertainty: An Examination of Stochastic Theory, Methods, and Applications, is a volume undertaken by the friends and colleagues of Sid Yakowitz in his honor. Fifty internationally known scholars have collectively contributed 30 papers on modeling uncertainty to this volume. Each of these papers was carefully reviewed and in the majority of cases the original submission was revised before being accepted for publication in the book. The papers cover a great variety of topics in probability, statistics, economics, stochastic optimization, control theory, regression analysis, simulation, stochastic programming, Markov decision process, application in the HIV context, and others. There are papers with a theoretical emphasis and others that focus on applications. A number of papers survey the work in a particular area and in a few papers the authors present their personal view of a topic. It is a book with a considerable number of expository articles, which are accessible to a nonexpert - a graduate student in mathematics, statistics, engineering, and economics departments, or just anyone with some mathematical background who is interested in a preliminary exposition of a particular topic. Many of the papers present the state of the art of a specific area or represent original contributions which advance the present state of knowledge. In sum, it is a book of considerable interest to a broad range of academic researchers and students of stochastic systems.

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.

When compared to classical sciences such as math, with roots in prehistory, and physics, with roots in antiquity, geographical information science (GISci) is the new kid on the block. Its theoretical foundations are therefore still developing and data quality and uncertainty modeling for spatial data and spatial analysis is an important branch of t

"This book provides the reader with basic concepts for soft computing and other methods for various means of uncertainty in handling solutions, analysis, and applications"--Provided by publisher.

Based on the research that has been conducted at Wharton Risk Management Center over the past five years on catastrophic risk. Covers a hot topic in the light of recent terroristic activities and nature catastrophes. Develops risk management strategies for reducing and spreading the losses from future disasters. Provides glossary of definitions and terms used throughout the book.

Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics, 2020, the third volume of nine from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Model Validation and Uncertainty Quantification, including papers on: Uncertainty Quantification in Material Models Uncertainty Propagation in Structural Dynamics Practical Applications of MVUQ Advances in Model Validation & Uncertainty Quantification: Model Updating Model Validation & Uncertainty Quantification: Industrial Applications Controlling Uncertainty Uncertainty in Early Stage Design Modeling of Musical Instruments Overview of Model Validation and Uncertainty

Modeling uncertainty for future prediction requires drawing multiple posterior models. Such drawing within a Bayesian framework is dependent on the likelihood (data-model relationship) as well as prior distribution of the model variables, For the uncertainty assessment in the Earth models, we propose the framework of Modeling Uncertainty in Metric Space (MUMS) to achieve this in a general way. MUMS constructs a metric space where the models are represented exclusively by a distance correlated with or equal to the difference in their responses (application-tailored distance). In the framework of MUMS, various operations are available: projection of metric space by multi-dimensional scaling, model expansion by kernel Karhunen-Loeve expansion, generation of additional prior model by solving the pre-image problem, and generation of multiple posterior models by solving the post-image problem. We propose a robust solution for the pre-image problem: geologically constrained optimization, which utilizes the probability perturbation method from the solution of the fixed-point iteration algorithm. Additionally, we introduce a so-called post-image problem for obtaining the feature expansion of the ''true Earth'' by defining a distance as the difference in their responses. The combination of geologically constrained optimization and the post-image problem efficiently generates multiple posterior Earth models constrained to prior geologic information, hard data, and nonlinear time-dependent data. The proposed method provides a realistic uncertainty model for future prediction, compared with the result of the rejection sampler. We also propose a metric ensemble Kalman filter (Metric EnKF), which applies the ensemble Kalman filter (EnKF) to the parameterizations by the kernel KL expansion in metric space. Metric EnKF overcomes some critical limitations of EnKF: it preserves prior geologic information; it creates a stable and consistent filtering. However, the results of Metric EnKF applied to various cases including the Brugge field-scale synthetic reservoir show the same problem as with the EnKF in general, that is, it does not provide a realistic uncertainty model.

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. Read an interview with the editors to find out more: https://eos.org/editors-vox/reducing-uncertainty-in-hazard-prediction