Chance And Uncertainty
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| Author | : Jim Albert |
| Publisher | : CRC Press |
| Total Pages | : 553 |
| Release | : 2019-12-06 |
| Genre | : Mathematics |
| ISBN | : 1351030132 |
Probability and Bayesian Modeling is an introduction to probability and Bayesian thinking for undergraduate students with a calculus background. The first part of the book provides a broad view of probability including foundations, conditional probability, discrete and continuous distributions, and joint distributions. Statistical inference is presented completely from a Bayesian perspective. The text introduces inference and prediction for a single proportion and a single mean from Normal sampling. After fundamentals of Markov Chain Monte Carlo algorithms are introduced, Bayesian inference is described for hierarchical and regression models including logistic regression. The book presents several case studies motivated by some historical Bayesian studies and the authors’ research. This text reflects modern Bayesian statistical practice. Simulation is introduced in all the probability chapters and extensively used in the Bayesian material to simulate from the posterior and predictive distributions. One chapter describes the basic tenets of Metropolis and Gibbs sampling algorithms; however several chapters introduce the fundamentals of Bayesian inference for conjugate priors to deepen understanding. Strategies for constructing prior distributions are described in situations when one has substantial prior information and for cases where one has weak prior knowledge. One chapter introduces hierarchical Bayesian modeling as a practical way of combining data from different groups. There is an extensive discussion of Bayesian regression models including the construction of informative priors, inference about functions of the parameters of interest, prediction, and model selection. The text uses JAGS (Just Another Gibbs Sampler) as a general-purpose computational method for simulating from posterior distributions for a variety of Bayesian models. An R package ProbBayes is available containing all of the book datasets and special functions for illustrating concepts from the book. A complete solutions manual is available for instructors who adopt the book in the Additional Resources section.
| Author | : Jeffrey A. Friedman |
| Publisher | : Oxford University Press |
| Total Pages | : 241 |
| Release | : 2019-04-01 |
| Genre | : Political Science |
| ISBN | : 019093803X |
Uncertainty surrounds every major decision in international politics. Yet there is almost always room for reasonable people to disagree about what that uncertainty entails. No one can reliably predict the outbreak of armed conflict, forecast economic recessions, anticipate terrorist attacks, or estimate the countless other risks that shape foreign policy choices. Many scholars and practitioners therefore believe that it is better to keep foreign policy debates focused on the facts - that it is, at best, a waste of time to debate uncertain judgments that will often prove to be wrong. In War and Chance, Jeffrey A. Friedman shows how foreign policy officials often try to avoid the challenge of assessing uncertainty, and argues that this behavior undermines high-stakes decision making. Drawing on an innovative combination of historical and experimental evidence, he explains how foreign policy analysts can assess uncertainty in a manner that is theoretically coherent, empirically meaningful, politically defensible, practically useful, and sometimes logically necessary for making sound choices. Each of these claims contradicts widespread skepticism about the value of probabilistic reasoning in international politics, and shows how placing greater emphasis on assessing uncertainty can improve nearly any foreign policy debate. A clear-eyed examination of the logic, psychology, and politics of assessing uncertainty, War and Chance provides scholars and practitioners with new foundations for understanding one of the most controversial elements of foreign policy discourse.
| Author | : John Tabak |
| Publisher | : Infobase Publishing |
| Total Pages | : 241 |
| Release | : 2014-05-14 |
| Genre | : Electronic books |
| ISBN | : 0816068739 |
Presents a survey of the history and evolution of the branch of mathematics that focuses on probability and statistics, including useful applications and notable mathematicians in this area.
| Author | : Michael J. Evans |
| Publisher | : Macmillan |
| Total Pages | : 704 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 9780716747420 |
Unlike traditional introductory math/stat textbooks, Probability and Statistics: The Science of Uncertainty brings a modern flavor based on incorporating the computer to the course and an integrated approach to inference. From the start the book integrates simulations into its theoretical coverage, and emphasizes the use of computer-powered computation throughout.* Math and science majors with just one year of calculus can use this text and experience a refreshing blend of applications and theory that goes beyond merely mastering the technicalities. They'll get a thorough grounding in probability theory, and go beyond that to the theory of statistical inference and its applications. An integrated approach to inference is presented that includes the frequency approach as well as Bayesian methodology. Bayesian inference is developed as a logical extension of likelihood methods. A separate chapter is devoted to the important topic of model checking and this is applied in the context of the standard applied statistical techniques. Examples of data analyses using real-world data are presented throughout the text. A final chapter introduces a number of the most important stochastic process models using elementary methods. *Note: An appendix in the book contains Minitab code for more involved computations. The code can be used by students as templates for their own calculations. If a software package like Minitab is used with the course then no programming is required by the students.
| Author | : William Briggs |
| Publisher | : Springer |
| Total Pages | : 274 |
| Release | : 2016-07-15 |
| Genre | : Mathematics |
| ISBN | : 3319397567 |
This book presents a philosophical approach to probability and probabilistic thinking, considering the underpinnings of probabilistic reasoning and modeling, which effectively underlie everything in data science. The ultimate goal is to call into question many standard tenets and lay the philosophical and probabilistic groundwork and infrastructure for statistical modeling. It is the first book devoted to the philosophy of data aimed at working scientists and calls for a new consideration in the practice of probability and statistics to eliminate what has been referred to as the "Cult of Statistical Significance." The book explains the philosophy of these ideas and not the mathematics, though there are a handful of mathematical examples. The topics are logically laid out, starting with basic philosophy as related to probability, statistics, and science, and stepping through the key probabilistic ideas and concepts, and ending with statistical models. Its jargon-free approach asserts that standard methods, such as out-of-the-box regression, cannot help in discovering cause. This new way of looking at uncertainty ties together disparate fields — probability, physics, biology, the “soft” sciences, computer science — because each aims at discovering cause (of effects). It broadens the understanding beyond frequentist and Bayesian methods to propose a Third Way of modeling.
| Author | : David F. Anderson |
| Publisher | : Cambridge University Press |
| Total Pages | : 447 |
| Release | : 2017-11-02 |
| Genre | : Mathematics |
| ISBN | : 110824498X |
This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.
| Author | : Michael A. Bean |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 464 |
| Release | : 2009 |
| Genre | : Mathematics |
| ISBN | : 0821847929 |
Covers the basic probability of distributions with an emphasis on applications from the areas of investments, insurance, and engineering. This book is suitable as a text for senior undergraduate and beginning graduate students in mathematics, statistics, actuarial science, finance, or engineering.
| Author | : |
| Publisher | : Allied Publishers |
| Total Pages | : 436 |
| Release | : 2013 |
| Genre | : |
| ISBN | : 9788177644517 |
| Author | : Andrew C. A. Elliott |
| Publisher | : Oxford University Press |
| Total Pages | : 483 |
| Release | : 2022-11-28 |
| Genre | : Mathematics |
| ISBN | : 0198883668 |
Chance fills every day of our lives and affects every decision we make. Yet, for something woven so closely into the fabric of our being, we are not very good at thinking about uncertainty and risk. In this lively and engaging book, Andrew C. A. Elliott asks why this is so. He picks at the threads and, in showing how our world is built on probability rather than certainty, he identifies five obstacles to thinking about uncertainty that confuse us time after time. Elliott takes us into the casino, but this is not an invitation to gamble. He looks at financial markets, but this is not a guide to investment. There's discussion of health, but this is not a medical book. He touches on genetics and evolution, and music-making, and writing, because chance is at work there too. Entering many different fields, What are the Chances of That? is always following the trail of chance and randomness. One purpose of the book is to go cross-country, to show that there are connected ways of thinking that disrespect boundaries and cut across the domains of finance, and gambling, and genetics, and public health, and creativity. Through it, one visits the vantage points that give a broad view of the landscape and sees how these different areas of life and knowledge are connected - through chance. What are the Chances of That? discusses chance and the importance of understanding how it affects our lives. It goes beyond a mathematical approach to the subject, showing how our thinking about chance and uncertainty has been shaped by history and culture, and only relatively recently by the mathematical theory of probability. In considering how we think about uncertainty, Elliott proposes five “dualities” that encapsulate many of the ambiguities that arise.
| Author | : Robin Willink |
| Publisher | : Cambridge University Press |
| Total Pages | : 295 |
| Release | : 2013-02-14 |
| Genre | : Science |
| ISBN | : 113961990X |
A measurement result is incomplete without a statement of its 'uncertainty' or 'margin of error'. But what does this statement actually tell us? By examining the practical meaning of probability, this book discusses what is meant by a '95 percent interval of measurement uncertainty', and how such an interval can be calculated. The book argues that the concept of an unknown 'target value' is essential if probability is to be used as a tool for evaluating measurement uncertainty. It uses statistical concepts, such as a conditional confidence interval, to present 'extended' classical methods for evaluating measurement uncertainty. The use of the Monte Carlo principle for the simulation of experiments is described. Useful for researchers and graduate students, the book also discusses other philosophies relating to the evaluation of measurement uncertainty. It employs clear notation and language to avoid the confusion that exists in this controversial field of science.
