understanding uncertainty wiley series in probability and statistics

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Understanding Uncertainty

Author : Dennis V. Lindley
ISBN : 9781118650127
Genre : Mathematics
File Size : 68. 62 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 : 9781119941651
Genre : Mathematics
File Size : 34. 99 MB
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Modelling has permeated virtually all areas of industrial, environmental, economic, bio-medical or civil engineering: yet the use of models for decision-making raises a number of issues to which this book is dedicated: How uncertain is my model ? Is it truly valuable to support decision-making ? What kind of decision can be truly supported and how can I handle residual uncertainty ? How much refined should the mathematical description be, given the true data limitations ? Could the uncertainty be reduced through more data, increased modeling investment or computational budget ? Should it be reduced now or later ? How robust is the analysis or the computational methods involved ? Should / could those methods be more robust ? Does it make sense to handle uncertainty, risk, lack of knowledge, variability or errors altogether ? How reasonable is the choice of probabilistic modeling for rare events ? How rare are the events to be considered ? How far does it make sense to handle extreme events and elaborate confidence figures ? Can I take advantage of expert / phenomenological knowledge to tighten the probabilistic figures ? Are there connex domains that could provide models or inspiration for my problem ? Written by a leader at the crossroads of industry, academia and engineering, and based on decades of multi-disciplinary field experience, Modelling Under Risk and Uncertainty gives a self-consistent introduction to the methods involved by any type of modeling development acknowledging the inevitable uncertainty and associated risks. It goes beyond the “black-box” view that some analysts, modelers, risk experts or statisticians develop on the underlying phenomenology of the environmental or industrial processes, without valuing enough their physical properties and inner modelling potential nor challenging the practical plausibility of mathematical hypotheses; conversely it is also to attract environmental or engineering modellers to better handle model confidence issues through finer statistical and risk analysis material taking advantage of advanced scientific computing, to face new regulations departing from deterministic design or support robust decision-making. Modelling Under Risk and Uncertainty: Addresses a concern of growing interest for large industries, environmentalists or analysts: robust modeling for decision-making in complex systems. Gives new insights into the peculiar mathematical and computational challenges generated by recent industrial safety or environmental control analysis for rare events. Implements decision theory choices differentiating or aggregating the dimensions of risk/aleatory and epistemic uncertainty through a consistent multi-disciplinary set of statistical estimation, physical modelling, robust computation and risk analysis. Provides an original review of the advanced inverse probabilistic approaches for model identification, calibration or data assimilation, key to digest fast-growing multi-physical data acquisition. Illustrated with one favourite pedagogical example crossing natural risk, engineering and economics, developed throughout the book to facilitate the reading and understanding. Supports Master/PhD-level course as well as advanced tutorials for professional training Analysts and researchers in numerical modeling, applied statistics, scientific computing, reliability, advanced engineering, natural risk or environmental science will benefit from this book.

Foundations Of Risk Analysis

Author : Terje Aven
ISBN : 9781119945789
Genre : Mathematics
File Size : 20. 52 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.

Understanding Statistical Error

Author : Marek Gierlinski
ISBN : 9781119106913
Genre : Medical
File Size : 43. 74 MB
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This accessible introductory textbook provides a straightforward, practical explanation of how statistical analysis and error measurements should be applied in biological research. Understanding Statistical Error - A Primer for Biologists: Introduces the essential topic of error analysis to biologists Contains mathematics at a level that all biologists can grasp Presents the formulas required to calculate each confidence interval for use in practice Is based on a successful series of lectures from the author’s established course Assuming no prior knowledge of statistics, this book covers the central topics needed for efficient data analysis, ranging from probability distributions, statistical estimators, confidence intervals, error propagation and uncertainties in linear regression, to advice on how to use error bars in graphs properly. Using simple mathematics, all these topics are carefully explained and illustrated with figures and worked examples. The emphasis throughout is on visual representation and on helping the reader to approach the analysis of experimental data with confidence. This useful guide explains how to evaluate uncertainties of key parameters, such as the mean, median, proportion and correlation coefficient. Crucially, the reader will also learn why confidence intervals are important and how they compare against other measures of uncertainty. Understanding Statistical Error - A Primer for Biologists can be used both by students and researchers to deepen their knowledge and find practical formulae to carry out error analysis calculations. It is a valuable guide for students, experimental biologists and professional researchers in biology, biostatistics, computational biology, cell and molecular biology, ecology, biological chemistry, drug discovery, biophysics, as well as wider subjects within life sciences and any field where error analysis is required.

Uncertain Judgements

Author : Anthony O'Hagan
ISBN : 9780470033302
Genre : Mathematics
File Size : 77. 48 MB
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Elicitation is the process of extracting expert knowledge about some unknown quantity or quantities, and formulating that information as a probability distribution. Elicitation is important in situations, such as modelling the safety of nuclear installations or assessing the risk of terrorist attacks, where expert knowledge is essentially the only source of good information. It also plays a major role in other contexts by augmenting scarce observational data, through the use of Bayesian statistical methods. However, elicitation is not a simple task, and practitioners need to be aware of a wide range of research findings in order to elicit expert judgements accurately and reliably. Uncertain Judgements introduces the area, before guiding the reader through the study of appropriate elicitation methods, illustrated by a variety of multi-disciplinary examples. This is achieved by: Presenting a methodological framework for the elicitation of expert knowledge incorporating findings from both statistical and psychological research. Detailing techniques for the elicitation of a wide range of standard distributions, appropriate to the most common types of quantities. Providing a comprehensive review of the available literature and pointing to the best practice methods and future research needs. Using examples from many disciplines, including statistics, psychology, engineering and health sciences. Including an extensive glossary of statistical and psychological terms. An ideal source and guide for statisticians and psychologists with interests in expert judgement or practical applications of Bayesian analysis, Uncertain Judgements will also benefit decision-makers, risk analysts, engineers and researchers in the medical and social sciences.

Approximate Dynamic Programming

Author : Warren B. Powell
ISBN : 0470182954
Genre : Mathematics
File Size : 66. 58 MB
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Willful Ignorance

Author : Herbert I. Weisberg
ISBN : 9781118593790
Genre : Mathematics
File Size : 27. 38 MB
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An original account of willful ignorance and how this principle relates to modern probability and statistical methods Through a series of colorful stories about great thinkers and the problems they chose to solve, the author traces the historical evolution of probability and explains how statistical methods have helped to propel scientific research. However, the past success of statistics has depended on vast, deliberate simplifications amounting to willful ignorance, and this very success now threatens future advances in medicine, the social sciences, and other fields. Limitations of existing methods result in frequent reversals of scientific findings and recommendations, to the consternation of both scientists and the lay public. Willful Ignorance: The Mismeasure of Uncertainty exposes the fallacy of regarding probability as the full measure of our uncertainty. The book explains how statistical methodology, though enormously productive and influential over the past century, is approaching a crisis. The deep and troubling divide between qualitative and quantitative modes of research, and between research and practice, are reflections of this underlying problem. The author outlines a path toward the re-engineering of data analysis to help close these gaps and accelerate scientific discovery. Willful Ignorance: The Mismeasure of Uncertainty presents essential information and novel ideas that should be of interest to anyone concerned about the future of scientific research. The book is especially pertinent for professionals in statistics and related fields, including practicing and research clinicians, biomedical and social science researchers, business leaders, and policy-makers.

Probability For Dummies

Author : Deborah J. Rumsey
ISBN : 9781118429099
Genre : Mathematics
File Size : 53. 53 MB
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Simplicity Complexity And Modelling

Author : Mike Christie
ISBN : 9781119960966
Genre : Mathematics
File Size : 62. 42 MB
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Several points of disagreement exist between different modelling traditions as to whether complex models are always better than simpler models, as to how to combine results from different models and how to propagate model uncertainty into forecasts. This book represents the result of collaboration between scientists from many disciplines to show how these conflicts can be resolved. Key Features: Introduces important concepts in modelling, outlining different traditions in the use of simple and complex modelling in statistics. Provides numerous case studies on complex modelling, such as climate change, flood risk and new drug development. Concentrates on varying models, including flood risk analysis models, the petrol industry forecasts and summarizes the evolution of water distribution systems. Written by experienced statisticians and engineers in order to facilitate communication between modellers in different disciplines. Provides a glossary giving terms commonly used in different modelling traditions. This book provides a much-needed reference guide to approaching statistical modelling. Scientists involved with modelling complex systems in areas such as climate change, flood prediction and prevention, financial market modelling and systems engineering will benefit from this book. It will also be a useful source of modelling case histories.

Principles Of Uncertainty

Author : Joseph B. Kadane
ISBN : 9781439861615
Genre : Mathematics
File Size : 71. 53 MB
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An intuitive and mathematical introduction to subjective probability and Bayesian statistics. An accessible, comprehensive guide to the theory of Bayesian statistics, Principles of Uncertainty presents the subjective Bayesian approach, which has played a pivotal role in game theory, economics, and the recent boom in Markov Chain Monte Carlo methods. Both rigorous and friendly, the book contains: Introductory chapters examining each new concept or assumption Just-in-time mathematics – the presentation of ideas just before they are applied Summary and exercises at the end of each chapter Discussion of maximization of expected utility The basics of Markov Chain Monte Carlo computing techniques Problems involving more than one decision-maker Written in an appealing, inviting style, and packed with interesting examples, Principles of Uncertainty introduces the most compelling parts of mathematics, computing, and philosophy as they bear on statistics. Although many books present the computation of a variety of statistics and algorithms while barely skimming the philosophical ramifications of subjective probability, this book takes a different tack. By addressing how to think about uncertainty, this book gives readers the intuition and understanding required to choose a particular method for a particular purpose.

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