understanding uncertainty wiley series in probability and statistics

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Understanding Uncertainty

Author : Dennis V. Lindley
ISBN : 9781118650127
Genre : Mathematics
File Size : 20. 28 MB
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Praise for the First Edition "...a reference for everyone who is interested in knowing and handling uncertainty." —Journal of Applied Statistics The critically acclaimed First Edition of Understanding Uncertainty provided a study of uncertainty addressed to scholars in all fields, showing that uncertainty could be measured by probability, and that probability obeyed three basic rules that enabled uncertainty to be handled sensibly in everyday life. These ideas were extended to embrace the scientific method and to show how decisions, containing an uncertain element, could be rationally made. Featuring new material, the Revised Edition remains the go-to guide for uncertainty and decision making, providing further applications at an accessible level including: A critical study of transitivity, a basic concept in probability A discussion of how the failure of the financial sector to use the proper approach to uncertainty may have contributed to the recent recession A consideration of betting, showing that a bookmaker's odds are not expressions of probability Applications of the book’s thesis to statistics A demonstration that some techniques currently popular in statistics, like significance tests, may be unsound, even seriously misleading, because they violate the rules of probability Understanding Uncertainty, Revised Edition is ideal for students studying probability or statistics and for anyone interested in one of the most fascinating and vibrant fields of study in contemporary science and mathematics.

Modelling Under Risk And Uncertainty

Author : Etienne de Rocquigny
ISBN : 9780470695142
Genre : Mathematics
File Size : 62. 8 MB
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"This volume addresses a concern of very high relevance and growing interest for large industries or environmentalists: risk and uncertainty in complex systems. It gives new insight on the peculiar mathematical challenges generated by recent industrial safety or environmental control analysis, focusing on implementing decision theory choices related to risk and uncertainty analysis through statistical estimation and computation, in the presence of physical modeling and risk analysis. The result will lead statisticians and associated professionals to formulate and solve new challenges at the frontier between statistical modeling, physics, scientific computing, and risk analysis"--

Foundations Of Risk Analysis

Author : Terje Aven
ISBN : 9781119945789
Genre : Mathematics
File Size : 71. 69 MB
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Foundations of Risk Analysis presents the issues core to risk analysis – understanding what risk means, expressing risk, building risk models, addressing uncertainty, and applying probability models to real problems. The author provides the readers with the knowledge and basic thinking they require to successfully manage risk and uncertainty to support decision making. This updated edition reflects recent developments on risk and uncertainty concepts, representations and treatment. New material in Foundations of Risk Analysis includes: An up to date presentation of how to understand, define and describe risk based on research carried out in recent years. A new definition of the concept of vulnerability consistent with the understanding of risk. Reflections on the need for seeing beyond probabilities to measure/describe uncertainties. A presentation and discussion of a method for assessing the importance of assumptions (uncertainty factors) in the background knowledge that the subjective probabilities are based on A brief introduction to approaches that produce interval (imprecise) probabilities instead of exact probabilities. In addition the new version provides a number of other improvements, for example, concerning the use of cost-benefit analyses and the As Low As Reasonably Practicable (ALARP) principle. Foundations of Risk Analysis provides a framework for understanding, conducting and using risk analysis suitable for advanced undergraduates, graduates, analysts and researchers from statistics, engineering, finance, medicine and the physical sciences, as well as for managers facing decision making problems involving risk and uncertainty.

Approximate Dynamic Programming

Author : Warren B. Powell
ISBN : 0470182954
Genre : Mathematics
File Size : 24. 5 MB
Format : PDF
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Geostatistics

Author : Jean-Paul Chilès
ISBN : 9781118136171
Genre : Mathematics
File Size : 74. 53 MB
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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.

Multiple Imputation For Nonresponse In Surveys

Author : Donald B. Rubin
ISBN : 9780470317365
Genre : Mathematics
File Size : 34. 54 MB
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Demonstrates how nonresponse in sample surveys and censuses can be handled by replacing each missing value with two or more multiple imputations. Clearly illustrates the advantages of modern computing to such handle surveys, and demonstrates the benefit of this statistical technique for researchers who must analyze them. Also presents the background for Bayesian and frequentist theory. After establishing that only standard complete-data methods are needed to analyze a multiply-imputed set, the text evaluates procedures in general circumstances, outlining specific procedures for creating imputations in both the ignorable and nonignorable cases. Examples and exercises reinforce ideas, and the interplay of Bayesian and frequentist ideas presents a unified picture of modern statistics.

An Introduction To Probability And Statistics

Author : Vijay K. Rohatgi
ISBN : 9781118799680
Genre : Mathematics
File Size : 46. 51 MB
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A well-balanced introduction to probability theory and mathematical statistics Featuring updated material, An Introduction to Probability and Statistics, Third Edition remains a solid overview to probability theory and mathematical statistics. Divided intothree parts, the Third Edition begins by presenting the fundamentals and foundationsof probability. The second part addresses statistical inference, and the remainingchapters focus on special topics. An Introduction to Probability and Statistics, Third Edition includes: A new section on regression analysis to include multiple regression, logistic regression, and Poisson regression A reorganized chapter on large sample theory to emphasize the growing role of asymptotic statistics Additional topical coverage on bootstrapping, estimation procedures, and resampling Discussions on invariance, ancillary statistics, conjugate prior distributions, and invariant confidence intervals Over 550 problems and answers to most problems, as well as 350 worked out examples and 200 remarks Numerous figures to further illustrate examples and proofs throughout An Introduction to Probability and Statistics, Third Edition is an ideal reference and resource for scientists and engineers in the fields of statistics, mathematics, physics, industrial management, and engineering. The book is also an excellent text for upper-undergraduate and graduate-level students majoring in probability and statistics.

Risk Analysis

Author : Terje Aven
ISBN : 0470694424
Genre : Mathematics
File Size : 64. 28 MB
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Everyday we face decisions that carry an element of risk and uncertainty. The ability to analyze, predict, and prepare for the level of risk entailed by these decisions is, therefore, one of the most constant and vital skills needed for analysts, scientists and managers. Risk analysis can be defined as a systematic use of information to identify hazards, threats and opportunities, as well as their causes and consequences, and then express risk. In order to successfully develop such a systematic use of information, those analyzing the risk need to understand the fundamental concepts of risk analysis and be proficient in a variety of methods and techniques. Risk Analysis adopts a practical, predictive approach and guides the reader through a number of applications. Risk Analysis: Provides an accessible and concise guide to performing risk analysis in a wide variety of fields, with minimal prior knowledge required. Adopts a broad perspective on risk, with focus on predictions and highlighting uncertainties beyond expected values and probabilities, allowing a more flexible approach than traditional statistical analysis. Acknowledges that expected values and probabilities could produce poor predictions - surprises may occur. Emphasizes the planning and use of risk analyses, rather than just the risk analysis methods and techniques, including the statistical analysis tools. Features many real-life case studies from a variety of applications and practical industry problems, including areas such as security, business and economy, transport, oil & gas and ICT (Information and Communication Technology). Forms an ideal companion volume to Aven’s previous Wiley text Foundations of Risk Analysis. Professor Aven’s previous book Foundations of Risk Analysis presented and discussed several risk analysis approaches and recommended a predictive approach. This new text expands upon this predictive approach, exploring further the risk analysis principles, concepts, methods and models in an applied format. This book provides a useful and practical guide to decision-making, aimed at professionals within the risk analysis and risk management field.

Spatial And Spatio Temporal Bayesian Models With R Inla

Author : Marta Blangiardo
ISBN : 9781118950210
Genre : Mathematics
File Size : 61. 68 MB
Format : PDF
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Spatial and Spatio-Temporal Bayesian Models with R-INLA provides a much needed, practically oriented & innovative presentation of the combination of Bayesian methodology and spatial statistics. The authors combine an introduction to Bayesian theory and methodology with a focus on the spatial and spatio­-temporal models used within the Bayesian framework and a series of practical examples which allow the reader to link the statistical theory presented to real data problems. The numerous examples from the fields of epidemiology, biostatistics and social science all are coded in the R package R-INLA, which has proven to be a valid alternative to the commonly used Markov Chain Monte Carlo simulations

Statistics For Spatio Temporal Data

Author : Noel Cressie
ISBN : 9781119243069
Genre : Mathematics
File Size : 46. 50 MB
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Winner of the 2013 DeGroot Prize. A state-of-the-art presentation of spatio-temporal processes, bridging classic ideas with modern hierarchical statistical modeling concepts and the latest computational methods Noel Cressie and Christopher K. Wikle, are also winners of the 2011 PROSE Award in the Mathematics category, for the book “Statistics for Spatio-Temporal Data” (2011), published by John Wiley and Sons. (The PROSE awards, for Professional and Scholarly Excellence, are given by the Association of American Publishers, the national trade association of the US book publishing industry.) Statistics for Spatio-Temporal Data has now been reprinted with small corrections to the text and the bibliography. The overall content and pagination of the new printing remains the same; the difference comes in the form of corrections to typographical errors, editing of incomplete and missing references, and some updated spatio-temporal interpretations. From understanding environmental processes and climate trends to developing new technologies for mapping public-health data and the spread of invasive-species, there is a high demand for statistical analyses of data that take spatial, temporal, and spatio-temporal information into account. Statistics for Spatio-Temporal Data presents a systematic approach to key quantitative techniques that incorporate the latest advances in statistical computing as well as hierarchical, particularly Bayesian, statistical modeling, with an emphasis on dynamical spatio-temporal models. Cressie and Wikle supply a unique presentation that incorporates ideas from the areas of time series and spatial statistics as well as stochastic processes. Beginning with separate treatments of temporal data and spatial data, the book combines these concepts to discuss spatio-temporal statistical methods for understanding complex processes. Topics of coverage include: Exploratory methods for spatio-temporal data, including visualization, spectral analysis, empirical orthogonal function analysis, and LISAs Spatio-temporal covariance functions, spatio-temporal kriging, and time series of spatial processes Development of hierarchical dynamical spatio-temporal models (DSTMs), with discussion of linear and nonlinear DSTMs and computational algorithms for their implementation Quantifying and exploring spatio-temporal variability in scientific applications, including case studies based on real-world environmental data Throughout the book, interesting applications demonstrate the relevance of the presented concepts. Vivid, full-color graphics emphasize the visual nature of the topic, and a related FTP site contains supplementary material. Statistics for Spatio-Temporal Data is an excellent book for a graduate-level course on spatio-temporal statistics. It is also a valuable reference for researchers and practitioners in the fields of applied mathematics, engineering, and the environmental and health sciences.

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