Economists have always recognised that human endeavours are constrained by our limited and uncertain knowledge, but only recently has an accepted theory of uncertainty and information evolved. This theory has turned out to have surprisingly practical applications: for example in analysing stock market returns, in evaluating accident prevention measures, and in assessing patent and copyright laws. This book presents these intellectual advances in readable form for the first time. It unifies many important but partial results into a satisfying single picture, making it clear how the economics of uncertainty and information generalises and extends standard economic analysis. Part One of the volume covers the economics of uncertainty: how each person adapts to a given fixed state of knowledge by making an optimal choice among the immediate 'terminal' actions available. These choices in turn determine the overall market equilibrium reflecting the social distribution of risk bearing. In Part Two, covering the economics of information, the state of knowledge is no longer held fixed. Instead, individuals can to a greater or lesser extent overcome their ignorance by 'informational' actions. The text also addresses at appropriate points many specific topics such as insurance, the Capital Asset Pricing model, auctions, deterrence of entry, and research and invention.
There has been explosive progress in the economic theory of uncertainty and information in the past few decades. This subject is now taught not only in departments of economics but also in professional schools and programs oriented toward business, government and administration, and public policy. This book attempts to unify the subject matter in a simple, accessible manner. Part I of the book focuses on the economics of uncertainty; Part II examines the economics of information. This revised and updated second edition places a greater focus on game theory. New topics include posted-price markets, mechanism design, common-value auctions, and the one-shot deviation principle for repeated games.
The amount of new information is constantly increasing, faster than our ability to fully interpret and utilize it to improve human experiences. Addressing this asymmetry requires novel and revolutionary scientific methods and effective human and artificial intelligence interfaces. By lifting the concept of time from a positive real number to a 2D complex time (kime), this book uncovers a connection between artificial intelligence (AI), data science, and quantum mechanics. It proposes a new mathematical foundation for data science based on raising the 4D spacetime to a higher dimension where longitudinal data (e.g., time-series) are represented as manifolds (e.g., kime-surfaces). This new framework enables the development of innovative data science analytical methods for model-based and model-free scientific inference, derived computed phenotyping, and statistical forecasting. The book provides a transdisciplinary bridge and a pragmatic mechanism to translate quantum mechanical principles, such as particles and wavefunctions, into data science concepts, such as datum and inference-functions. It includes many open mathematical problems that still need to be solved, technological challenges that need to be tackled, and computational statistics algorithms that have to be fully developed and validated. Spacekime analytics provide mechanisms to effectively handle, process, and interpret large, heterogeneous, and continuously-tracked digital information from multiple sources. The authors propose computational methods, probability model-based techniques, and analytical strategies to estimate, approximate, or simulate the complex time phases (kime directions). This allows transforming time-varying data, such as time-series observations, into higher-dimensional manifolds representing complex-valued and kime-indexed surfaces (kime-surfaces). The book includes many illustrations of model-based and model-free spacekime analytic techniques applied to economic forecasting, identification of functional brain activation, and high-dimensional cohort phenotyping. Specific case-study examples include unsupervised clustering using the Michigan Consumer Sentiment Index (MCSI), model-based inference using functional magnetic resonance imaging (fMRI) data, and model-free inference using the UK Biobank data archive. The material includes mathematical, inferential, computational, and philosophical topics such as Heisenberg uncertainty principle and alternative approaches to large sample theory, where a few spacetime observations can be amplified by a series of derived, estimated, or simulated kime-phases. The authors extend Newton-Leibniz calculus of integration and differentiation to the spacekime manifold and discuss possible solutions to some of the "problems of time". The coverage also includes 5D spacekime formulations of classical 4D spacetime mathematical equations describing natural laws of physics, as well as, statistical articulation of spacekime analytics in a Bayesian inference framework. The steady increase of the volume and complexity of observed and recorded digital information drives the urgent need to develop novel data analytical strategies. Spacekime analytics represents one new data-analytic approach, which provides a mechanism to understand compound phenomena that are observed as multiplex longitudinal processes and computationally tracked by proxy measures. This book may be of interest to academic scholars, graduate students, postdoctoral fellows, artificial intelligence and machine learning engineers, biostatisticians, econometricians, and data analysts. Some of the material may also resonate with philosophers, futurists, astrophysicists, space industry technicians, biomedical researchers, health practitioners, and the general public.
Inverse problems are found in many applications, such as medical imaging, engineering, astronomy, and geophysics, among others. To solve an inverse problem is to recover an object from noisy, usually indirect observations. Solutions to inverse problems are subject to many potential sources of error introduced by approximate mathematical models, regularization methods, numerical approximations for efficient computations, noisy data, and limitations in the number of observations; thus it is important to include an assessment of the uncertainties as part of the solution. Such assessment is interdisciplinary by nature, as it requires, in addition to knowledge of the particular application, methods from applied mathematics, probability, and statistics. This book bridges applied mathematics and statistics by providing a basic introduction to probability and statistics for uncertainty quantification in the context of inverse problems, as well as an introduction to statistical regularization of inverse problems. The author covers basic statistical inference, introduces the framework of ill-posed inverse problems, and explains statistical questions that arise in their applications. An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems?includes many examples that explain techniques which are useful to address general problems arising in uncertainty quantification, Bayesian and non-Bayesian statistical methods and discussions of their complementary roles, and analysis of a real data set to illustrate the methodology covered throughout the book.
Essential Microeconomics is designed to help students deepen their understanding of the core theory of microeconomics. Unlike other texts, this book focuses on the most important ideas and does not attempt to be encyclopedic. Two-thirds of the textbook focuses on price theory. As well as taking a new look at standard equilibrium theory, there is extensive examination of equilibrium under uncertainty, the capital asset pricing model, and arbitrage pricing theory. Choice over time is given extensive coverage and includes a basic introduction to control theory. The final third of the book, on game theory, provides a comprehensive introduction to models with asymmetric information. Topics such as auctions, signaling, and mechanism design are made accessible to students who have a basic rather than a deep understanding of mathematics. There is ample use of examples and diagrams to illustrate issues as well as formal derivations. Essential Microeconomics is designed to help students deepen their understanding of the core theory of microeconomics.
Build the skills for determining appropriate error limits for quantities that matter with this essential toolkit. Understand how to handle a complete project and how uncertainty enters into various steps. Provides a systematic, worksheet-based process to determine error limits on measured quantities, and all likely sources of uncertainty are explored, measured or estimated. Features instructions on how to carry out error analysis using Excel and MATLAB®, making previously tedious calculations easy. Whether you are new to the sciences or an experienced engineer, this useful resource provides a practical approach to performing error analysis. Suitable as a text for a junior or senior level laboratory course in aerospace, chemical and mechanical engineering, and for professionals.
Risks and uncertainties?market, financial, operational, social, humanitarian, environmental, and institutional?are the inherent realities of the modern world. Stock market crashes, demonetization of currency, and climate change constitute just a few examples that can adversely impact financial institutions across the globe. To mitigate these risks and avoid a financial crisis, a better understanding of how the economy responds to uncertainties is needed. Maintaining Financial Stability in Times of Risk and Uncertainty is an essential reference source that discusses how risks and uncertainties affect the financial stability and security of individuals and institutions, as well as probable solutions to mitigate risk and achieve financial resilience under uncertainty. Featuring research on topics such as financial fraud, insurance ombudsman, and Knightian uncertainty, this book is developed for researchers, academicians, policymakers, students, and scholars.
This textbook teaches the essential background and skills for understanding and quantifying uncertainties in a computational simulation, and for predicting the behavior of a system under those uncertainties. It addresses a critical knowledge gap in the widespread adoption of simulation in high-consequence decision-making throughout the engineering and physical sciences. Constructing sophisticated techniques for prediction from basic building blocks, the book first reviews the fundamentals that underpin later topics of the book including probability, sampling, and Bayesian statistics. Part II focuses on applying Local Sensitivity Analysis to apportion uncertainty in the model outputs to sources of uncertainty in its inputs. Part III demonstrates techniques for quantifying the impact of parametric uncertainties on a problem, specifically how input uncertainties affect outputs. The final section covers techniques for applying uncertainty quantification to make predictions under uncertainty, including treatment of epistemic uncertainties. It presents the theory and practice of predicting the behavior of a system based on the aggregation of data from simulation, theory, and experiment. The text focuses on simulations based on the solution of systems of partial differential equations and includes in-depth coverage of Monte Carlo methods, basic design of computer experiments, as well as regularized statistical techniques. Code references, in python, appear throughout the text and online as executable code, enabling readers to perform the analysis under discussion. Worked examples from realistic, model problems help readers understand the mechanics of applying the methods. Each chapter ends with several assignable problems. Uncertainty Quantification and Predictive Computational Science fills the growing need for a classroom text for senior undergraduate and early-career graduate students in the engineering and physical sciences and supports independent study by researchers and professionals who must include uncertainty quantification and predictive science in the simulations they develop and/or perform.
Introduction to Business Analytics Using Simulation, Second Edition employs an innovative strategy to teach business analytics. The book uses simulation modeling and analysis as mechanisms to introduce and link predictive and prescriptive modeling. Because managers can't fully assess what will happen in the future, but must still make decisions, the book treats uncertainty as an essential element in decision-making. Its use of simulation gives readers a superior way of analyzing past data, understanding an uncertain future, and optimizing results to select the best decision. With its focus on uncertainty and variability, this book provides a comprehensive foundation for business analytics. Students will gain a better understanding of fundamental statistical concepts that are essential to marketing research, Six-Sigma, financial analysis, and business analytics. - Teaches managers how they can use business analytics to formulate and solve business problems to enhance managerial decision-making - Explains the processes needed to develop, report and analyze business data - Describes how to use and apply business analytics software - Offers expanded coverage on the value and application of prescriptive analytics - Includes a wealth of illustrative exercises that are newly organized by difficulty level - Winner of the 2017 Textbook and Academic Authors Association's (TAA) Most Promising New Textbook Award in the prior edition
This book describes what Intelligence Community (IC) analysts do, how they do it, and how they are affected by the political context that shapes, uses, and sometimes abuses their output. It is written by a 25-year intelligence professional.
