Probability Choice And Reason

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Probability, Choice, and Reason

Author : Leighton Vaughan Williams
Publisher : CRC Press
Page : 311 pages
File Size : 41,7 Mb
Release : 2021-09-15
Category : Mathematics
ISBN : 9781000458879

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Probability, Choice, and Reason by Leighton Vaughan Williams Pdf

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.

Probability, Choice, and Reason

Author : Leighton Vaughan Williams
Publisher : CRC Press
Page : 180 pages
File Size : 43,9 Mb
Release : 2021-09-16
Category : Mathematics
ISBN : 9781000458947

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Probability, Choice, and Reason by Leighton Vaughan Williams Pdf

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.

Cognition and Chance

Author : Raymond S. Nickerson
Publisher : Psychology Press
Page : 450 pages
File Size : 46,5 Mb
Release : 2004-06-24
Category : Business & Economics
ISBN : 9781135614621

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Cognition and Chance by Raymond S. Nickerson Pdf

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,

Toward Robots That Reason: Logic, Probability & Causal Laws

Author : Vaishak Belle
Publisher : Springer Nature
Page : 201 pages
File Size : 47,5 Mb
Release : 2023-02-20
Category : Computers
ISBN : 9783031210037

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Toward Robots That Reason: Logic, Probability & Causal Laws by Vaishak Belle Pdf

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.

The Science of Reason

Author : Ken Manktelow,David Over,Shira Elqayam
Publisher : Psychology Press
Page : 473 pages
File Size : 43,6 Mb
Release : 2010-10-18
Category : Psychology
ISBN : 9781136939099

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The Science of Reason by Ken Manktelow,David Over,Shira Elqayam Pdf

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.

The Probability of God

Author : Dr. Stephen D. Unwin
Publisher : Forum Books
Page : 274 pages
File Size : 51,6 Mb
Release : 2004-10-26
Category : Religion
ISBN : 9781400054787

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The Probability of God by Dr. Stephen D. Unwin Pdf

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

Improving Bayesian Reasoning: What Works and Why?

Author : Gorka Navarrete,David R. Mandel
Publisher : Frontiers Media SA
Page : 209 pages
File Size : 55,7 Mb
Release : 2016-02-02
Category : Electronic book
ISBN : 9782889197453

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Improving Bayesian Reasoning: What Works and Why? by Gorka Navarrete,David R. Mandel Pdf

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.

Aggregation Functions in Theory and in Practise

Author : Humberto Bustince Sola,Javier Fernandez,Radko Mesiar,Tomasa Calvo
Publisher : Springer Science & Business Media
Page : 535 pages
File Size : 44,7 Mb
Release : 2013-06-20
Category : Technology & Engineering
ISBN : 9783642391651

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Aggregation Functions in Theory and in Practise by Humberto Bustince Sola,Javier Fernandez,Radko Mesiar,Tomasa Calvo Pdf

This volume collects the extended abstracts of 45 contributions of participants to the Seventh International Summer School on Aggregation Operators (AGOP 2013), held at Pamplona in July, 16-20, 2013. These contributions cover a very broad range, from the purely theoretical ones to those with a more applied focus. Moreover, the summaries of the plenary talks and tutorials given at the same workshop are included. Together they provide a good overview of recent trends in research in aggregation functions which can be of interest to both researchers in Physics or Mathematics working on the theoretical basis of aggregation functions, and to engineers who require them for applications.

The Roots of Reason

Author : David Papineau
Publisher : Oxford University Press
Page : 260 pages
File Size : 55,9 Mb
Release : 2006-01-26
Category : Mathematics
ISBN : 0199288712

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The Roots of Reason by David Papineau Pdf

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 theradical 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.

Decision, Probability and Utility

Author : Peter Gärdenfors,Nils-Eric Sahlin
Publisher : Cambridge University Press
Page : 464 pages
File Size : 41,9 Mb
Release : 1988-04-29
Category : Business & Economics
ISBN : 0521336589

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Decision, Probability and Utility by Peter Gärdenfors,Nils-Eric Sahlin Pdf

Decision theory and the theory of rational choice have recently been the subjects of considerable research by philosophers and economists. However, no adequate anthology exists which can be used to introduce students to the field. This volume is designed to meet that need. The essays included are organized into five parts covering the foundations of decision theory, the conceptualization of probability and utility, pholosophical difficulties with the rules of rationality and with the assessment of probability, and causal decision theory. The editors provide an extensive introduction to the field and introductions to each part.

Philosophical Theories of Probability

Author : Donald Gillies
Publisher : Routledge
Page : 239 pages
File Size : 53,5 Mb
Release : 2012-09-10
Category : Philosophy
ISBN : 9781134672455

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Philosophical Theories of Probability by Donald Gillies Pdf

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.

Probability Theory

Author : Nikolai Dokuchaev
Publisher : World Scientific Publishing Company
Page : 224 pages
File Size : 45,9 Mb
Release : 2015-06-12
Category : Business & Economics
ISBN : 9789814678056

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Probability Theory by Nikolai Dokuchaev Pdf

This book provides a systematic, self-sufficient and yet short presentation of the mainstream topics on introductory Probability Theory with some selected topics from Mathematical Statistics. It is suitable for a 10- to 14-week course for second- or third-year undergraduate students in Science, Mathematics, Statistics, Finance, or Economics, who have completed some introductory course in Calculus. There is a sufficient number of problems and solutions to cover weekly tutorials.

Logic, Probability, and Presumptions in Legal Reasoning

Author : Scott Brewer
Publisher : Routledge
Page : 416 pages
File Size : 53,5 Mb
Release : 2013-06-17
Category : Philosophy
ISBN : 9781135642747

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Logic, Probability, and Presumptions in Legal Reasoning by Scott Brewer Pdf

At least since plato and Aristotle, thinkers have pondered the relationship between philosophical arguments and the "sophistical" arguments offered by the Sophists -- who were the first professional lawyers. Judges wield substantial political power, and the justifications they offer for their decisions are a vital means by which citizens can assess the legitimacy of how that power is exercised. However, to evaluate judicial justifications requires close attention to the method of reasoning behind decisions. This new collection illuminates and explains the political and moral importance in justifying the exercise of judicial power.

Paradoxes in Probability Theory

Author : William Eckhardt
Publisher : Springer Science & Business Media
Page : 85 pages
File Size : 48,9 Mb
Release : 2012-09-27
Category : Mathematics
ISBN : 9789400751392

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Paradoxes in Probability Theory by William Eckhardt Pdf

Paradoxes provide a vehicle for exposing misinterpretations and misapplications of accepted principles. This book discusses seven paradoxes surrounding probability theory. Some remain the focus of controversy; others have allegedly been solved, however the accepted solutions are demonstrably incorrect. Each paradox is shown to rest on one or more fallacies. Instead of the esoteric, idiosyncratic, and untested methods that have been brought to bear on these problems, the book invokes uncontroversial probability principles, acceptable both to frequentists and subjectivists. The philosophical disputation inspired by these paradoxes is shown to be misguided and unnecessary; for instance, startling claims concerning human destiny and the nature of reality are directly related to fallacious reasoning in a betting paradox, and a problem analyzed in philosophy journals is resolved by means of a computer program.​

Normative Reasons

Author : Artūrs Logins
Publisher : Cambridge University Press
Page : 253 pages
File Size : 47,7 Mb
Release : 2022-08-04
Category : Philosophy
ISBN : 9781316513774

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Normative Reasons by Artūrs Logins Pdf

The first accessible, detailed overview of the debates about normative reasons, developing a new theory based on why-questions.