Probability Choice And Reason

Author : Leighton Vaughan Williams
Publisher : CRC Press
ISBN 13 : 1000458873
Total Pages : 311 pages
Book Rating : 4.79/5 ( download)

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Download or read book Probability, Choice, and Reason written by Leighton Vaughan Williams and published by CRC Press. This book was released on 2021-09-15 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Much of our thinking is flawed because it is based on faulty intuition. By using the framework and tools of probability and statistics, we can overcome this to provide solutions to many real-world problems and paradoxes. We show how to do this, and find answers that are frequently very contrary to what we might expect. Along the way, we venture into diverse realms and thought experiments which challenge the way that we see the world. Features: An insightful and engaging discussion of some of the key ideas of probabilistic and statistical thinking Many classic and novel problems, paradoxes, and puzzles An exploration of some of the big questions involving the use of choice and reason in an uncertain world The application of probability, statistics, and Bayesian methods to a wide range of subjects, including economics, finance, law, and medicine Exercises, references, and links for those wishing to cross-reference or to probe further Solutions to exercises at the end of the book This book should serve as an invaluable and fascinating resource for university, college, and high school students who wish to extend their reading, as well as for teachers and lecturers who want to liven up their courses while retaining academic rigour. It will also appeal to anyone who wishes to develop skills with numbers or has an interest in the many statistical and other paradoxes that permeate our lives. Indeed, anyone studying the sciences, social sciences, or humanities on a formal or informal basis will enjoy and benefit from this book.

Author : Leighton Vaughan Williams
Publisher : CRC Press
ISBN 13 : 1000458946
Total Pages : 180 pages
Book Rating : 4.47/5 ( download)

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Download or read book Probability, Choice, and Reason written by Leighton Vaughan Williams and published by CRC Press. This book was released on 2021-09-16 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Much of our thinking is flawed because it is based on faulty intuition. By using the framework and tools of probability and statistics, we can overcome this to provide solutions to many real-world problems and paradoxes. We show how to do this, and find answers that are frequently very contrary to what we might expect. Along the way, we venture into diverse realms and thought experiments which challenge the way that we see the world. Features: An insightful and engaging discussion of some of the key ideas of probabilistic and statistical thinking Many classic and novel problems, paradoxes, and puzzles An exploration of some of the big questions involving the use of choice and reason in an uncertain world The application of probability, statistics, and Bayesian methods to a wide range of subjects, including economics, finance, law, and medicine Exercises, references, and links for those wishing to cross-reference or to probe further Solutions to exercises at the end of the book This book should serve as an invaluable and fascinating resource for university, college, and high school students who wish to extend their reading, as well as for teachers and lecturers who want to liven up their courses while retaining academic rigour. It will also appeal to anyone who wishes to develop skills with numbers or has an interest in the many statistical and other paradoxes that permeate our lives. Indeed, anyone studying the sciences, social sciences, or humanities on a formal or informal basis will enjoy and benefit from this book.

Author : Hugh Gordon
Publisher : Springer Science & Business Media
ISBN 13 : 1461219663
Total Pages : 272 pages
Book Rating : 4.68/5 ( download)

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Download or read book Discrete Probability written by Hugh Gordon and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended as a first course in probability at post-calculus level, this book is of special interest to students majoring in computer science as well as in mathematics. Since calculus is used only occasionally in the text, students who have forgotten their calculus can nevertheless easily understand the book, and its slow, gentle style and clear exposition will also appeal. Basic concepts such as counting, independence, conditional probability, random variables, approximation of probabilities, generating functions, random walks and Markov chains are all clearly explained and backed by many worked exercises. The 1,196 numerical answers to the 405 exercises, many with multiple parts, are included at the end of the book, and throughout, there are various historical comments on the study of probability. These include biographical information on such famous contributors as Fermat, Pascal, the Bernoullis, DeMoivre, Bayes, Laplace, Poisson, and Markov. Of interest to a wide range of readers and useful in many undergraduate programs.

Author : Dr. Stephen D. Unwin
Publisher : Forum Books
ISBN 13 : 1400054788
Total Pages : 274 pages
Book Rating : 4.87/5 ( download)

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Download or read book The Probability of God written by Dr. Stephen D. Unwin and published by Forum Books. This book was released on 2004-10-26 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Does God exist? This is probably the most debated question in the history of mankind. Scholars, scientists, and philosophers have spent their lifetimes trying to prove or disprove the existence of God, only to have their theories crucified by other scholars, scientists, and philosophers. Where the debate breaks down is in the ambiguities and colloquialisms of language. But, by using a universal, unambiguous language—namely, mathematics—can this question finally be answered definitively? That’s what Dr. Stephen Unwin attempts to do in this riveting, accessible, and witty book, The Probability of God. At its core, this groundbreaking book reveals how a math equation developed more than 200 years ago by noted European philosopher Thomas Bayes can be used to calculate the probability that God exists. The equation itself is much more complicated than a simple coin toss (heads, He’s up there running the show; tails, He’s not). Yet Dr. Unwin writes with a clarity that makes his mathematical proof easy for even the nonmathematician to understand and a verve that makes his book a delight to read. Leading you carefully through each step in his argument, he demonstrates in the end that God does indeed exist. Whether you’re a devout believer and agree with Dr. Unwin’s proof or are unsure about all things divine, you will find this provocative book enlightening and engaging. “One of the most innovative works [in the science and religion movement] is The Probability of God...An entertaining exercise in thinking.”—Michael Shermer, Scientific American “Unwin’s book [is] peppered with wry, self-deprecating humor that makes the scientific discussions more accessible...Spiritually inspiring.”--Chicago Sun Times “A pleasantly breezy account of some complicated matters well worth learning about.”--Philadelphia Inquirer “One of the best things about the book is its humor.”--Cleveland Plain Dealer “In a book that is surprisingly lighthearted and funny, Unwin manages to pack in a lot of facts about science and philosophy.”--Salt Lake Tribune

Author : Raymond S. Nickerson
Publisher : Psychology Press
ISBN 13 : 1135614628
Total Pages : 450 pages
Book Rating : 4.21/5 ( download)

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Download or read book Cognition and Chance written by Raymond S. Nickerson and published by Psychology Press. This book was released on 2004-06-24 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an overview of the necessary information needed to make educational assumptions about the statistical or probable characteristics of a situation. The book can be used as a supplemental text in courses on probability, logic, statistics,

Author : David Papineau
Publisher : OUP Oxford
ISBN 13 : 0191516082
Total Pages : 252 pages
Book Rating : 4.85/5 ( download)

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Download or read book The Roots of Reason written by David Papineau and published by OUP Oxford. This book was released on 2006-01-26 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: David Papineau presents a controversial view of human reason, portraying it as a normal part of the natural world, and drawing on the empirical sciences to illuminate its workings. In these six interconnected essays he offers a fresh approach to some long-standing problems. Papineau rejects the contemporary orthodoxy that genuine thought hinges on some species of non-natural normativity. He explores the evolutionary histories of theoretical and practical rationality, indicating ways in which capacities underlying human reasoning have been selected for their biological advantages. He then looks at the connection between decision and probability, explaining how good decisions need to be informed by causal as well as probabilistic facts. Finally he defends the radical view that a satisfactory understanding of decision-making is only possible within a specific interpretation of quantum mechanics. By placing the subject in its scientific context, Papineau shows how human rationality plays an explicable role in the functioning of the natural world.

Author : Vaishak Belle
Publisher : Springer Nature
ISBN 13 : 3031210034
Total Pages : 201 pages
Book Rating : 4.37/5 ( download)

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Download or read book Toward Robots That Reason: Logic, Probability & Causal Laws written by Vaishak Belle and published by Springer Nature. This book was released on 2023-02-20 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the two fundamental elements that underline the science and design of artificial intelligence (AI) systems: the learning and acquisition of knowledge from observational data, and the reasoning of that knowledge together with whatever information is available about the application at hand. It then presents a mathematical treatment of the core issues that arise when unifying first-order logic and probability, especially in the presence of dynamics, including physical actions, sensing actions and their effects. A model for expressing causal laws describing dynamics is also considered, along with computational ideas for reasoning with such laws over probabilistic logical knowledge.

Author : Ken Manktelow
Publisher : Psychology Press
ISBN 13 : 1136939091
Total Pages : 473 pages
Book Rating : 4.99/5 ( download)

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Download or read book The Science of Reason written by Ken Manktelow and published by Psychology Press. This book was released on 2010-10-18 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a state-of-the-art survey of the psychology of reasoning, based around, and in tribute to, one of the field’s most eminent figures: Jonathan St B.T. Evans. In this collection of cutting edge research, Evans’ collaborators and colleagues review a wide range of important and developing areas of inquiry. These include biases in thinking, probabilistic and causal reasoning, people’s use of ‘if’ sentences in arguments, the dual-process theory of thought, and the nature of human rationality. These foundational issues are examined from various angles and finally integrated in a concluding panoramic chapter written by Evans himself. The eighteen chapters, all written by leading international researchers, combine state-of the-art research with investigation into the most fundamental questions surrounding human mental life, such as: What is the architecture of the human mind? Are humans rational, and what is the nature of this rationality? How do we think hypothetically? The Science of Reason offers a unique combination of breadth, depth and integrative vision, making it an indispensable resource for researchers and students of human reason.

Author : Gorka Navarrete
Publisher : Frontiers Media SA
ISBN 13 : 288919745X
Total Pages : 209 pages
Book Rating : 4.53/5 ( download)

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Download or read book Improving Bayesian Reasoning: What Works and Why? written by Gorka Navarrete and published by Frontiers Media SA. This book was released on 2016-02-02 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: We confess that the first part of our title is somewhat of a misnomer. Bayesian reasoning is a normative approach to probabilistic belief revision and, as such, it is in need of no improvement. Rather, it is the typical individual whose reasoning and judgments often fall short of the Bayesian ideal who is the focus of improvement. What have we learnt from over a half-century of research and theory on this topic that could explain why people are often non-Bayesian? Can Bayesian reasoning be facilitated, and if so why? These are the questions that motivate this Frontiers in Psychology Research Topic. Bayes' theorem, named after English statistician, philosopher, and Presbyterian minister, Thomas Bayes, offers a method for updating one’s prior probability of an hypothesis H on the basis of new data D such that P(H|D) = P(D|H)P(H)/P(D). The first wave of psychological research, pioneered by Ward Edwards, revealed that people were overly conservative in updating their posterior probabilities (i.e., P(D|H)). A second wave, spearheaded by Daniel Kahneman and Amos Tversky, showed that people often ignored prior probabilities or base rates, where the priors had a frequentist interpretation, and hence were not Bayesians at all. In the 1990s, a third wave of research spurred by Leda Cosmides and John Tooby and by Gerd Gigerenzer and Ulrich Hoffrage showed that people can reason more like a Bayesian if only the information provided takes the form of (non-relativized) natural frequencies. Although Kahneman and Tversky had already noted the advantages of frequency representations, it was the third wave scholars who pushed the prescriptive agenda, arguing that there are feasible and effective methods for improving belief revision. Most scholars now agree that natural frequency representations do facilitate Bayesian reasoning. However, they do not agree on why this is so. The original third wave scholars favor an evolutionary account that posits human brain adaptation to natural frequency processing. But almost as soon as this view was proposed, other scholars challenged it, arguing that such evolutionary assumptions were not needed. The dominant opposing view has been that the benefit of natural frequencies is mainly due to the fact that such representations make the nested set relations perfectly transparent. Thus, people can more easily see what information they need to focus on and how to simply combine it. This Research Topic aims to take stock of where we are at present. Are we in a proto-fourth wave? If so, does it offer a synthesis of recent theoretical disagreements? The second part of the title orients the reader to the two main subtopics: what works and why? In terms of the first subtopic, we seek contributions that advance understanding of how to improve people’s abilities to revise their beliefs and to integrate probabilistic information effectively. The second subtopic centers on explaining why methods that improve non-Bayesian reasoning work as well as they do. In addressing that issue, we welcome both critical analyses of existing theories as well as fresh perspectives. For both subtopics, we welcome the full range of manuscript types.

Author : Donald Gillies
Publisher : Routledge
ISBN 13 : 1134672454
Total Pages : 239 pages
Book Rating : 4.55/5 ( download)

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Download or read book Philosophical Theories of Probability written by Donald Gillies and published by Routledge. This book was released on 2012-09-10 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Twentieth Century has seen a dramatic rise in the use of probability and statistics in almost all fields of research. This has stimulated many new philosophical ideas on probability. Philosophical Theories of Probability is the first book to present a clear, comprehensive and systematic account of these various theories and to explain how they relate to one another. Gillies also offers a distinctive version of the propensity theory of probability, and the intersubjective interpretation, which develops the subjective theory.