Bayes' Rule

A Tutorial Introduction to Bayesian Analysis

Author: James V. Stone

Publisher: Sebtel Press

ISBN: 0956372848

Category: Bayesian statistical decision theory

Page: 170

View: 6740

In this richly illustrated book, a range of accessible examples are used to show how Bayes' rule is actually a natural consequence of commonsense reasoning. The tutorial style of writing, combined with a comprehensive glossary, makes this an ideal primer for the novice who wishes to become familiar with the basic principles of Bayesian analysis.
Posted in Bayesian statistical decision theory

The Theory that Would Not Die

How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, & Emerged Triumphant from Two Centuries of Controversy

Author: Sharon Bertsch McGrayne

Publisher: Yale University Press

ISBN: 0300175094

Category: Mathematics

Page: 335

View: 2864

Bayes rule appears to be a straightforward, one-line theorem: by updating our initial beliefs with objective new information, we get a new and improved belief. To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok. In the first-ever account of Bayes' rule for general readers, Sharon Bertsch McGrayne explores this controversial theorem and the human obsessions surrounding it. She traces its discovery by an amateur mathematician in the 1740s through its development into roughly its modern form by French scientist Pierre Simon Laplace. She reveals why respected statisticians rendered it professionally taboo for 150 years at the same time that practitioners relied on it to solve crises involving great uncertainty and scanty information, even breaking Germany's Enigma code during World War II, and explains how the advent of off-the-shelf computer technology in the 1980s proved to be a game-changer. Today, Bayes' rule is used everywhere from DNA de-coding to Homeland Security.Drawing on primary source material and interviews with statisticians and other scientists, The Theory That Would Not Die is the riveting account of how a seemingly simple theorem ignited one of the greatest controversies of all time.
Posted in Mathematics

Bayes' Rule With R

A Tutorial Introduction to Bayesian Analysis

Author: James V Stone

Publisher: N.A

ISBN: 9780993367946

Category: Mathematics

Page: 186

View: 6192

Discovered by an 18th century mathematician and preacher, Bayes' rule is a cornerstone of modern probability theory. In this richly illustrated book, a range of accessible examples is used to show how Bayes' rule is actually a natural consequence of common sense reasoning. Bayes' rule is then derived using intuitive graphical representations of probability, and Bayesian analysis is applied to parameter estimation. The tutorial style of writing, combined with a comprehensive glossary, makes this an ideal primer for novices who wish to become familiar with the basic principles of Bayesian analysis. Note that this book includes R (3.2) code snippets, which reproduce key numerical results and diagrams.
Posted in Mathematics

Bayes' Rule with MatLab

A Tutorial Introduction to Bayesian Analysis

Author: James V Stone

Publisher: N.A

ISBN: 9780993367908

Category: Mathematics

Page: 192

View: 2448

Discovered by an 18th century mathematician and preacher, Bayes' rule is a cornerstone of modern probability theory. In this richly illustrated book, a range of accessible examples is used to show how Bayes' rule is actually a natural consequence of common sense reasoning. Bayes' rule is then derived using intuitive graphical representations of probability, and Bayesian analysis is applied to parameter estimation using the MatLab and Python programs provided online. The tutorial style of writing, combined with a comprehensive glossary, makes this an ideal primer for novices who wish to become familiar with the basic principles of Bayesian analysis. Note that this MatLab version of Bayes' Rule includes working MatLab code snippets alongside the relevant equations.
Posted in Mathematics

Improving Bayesian Reasoning: What Works and Why?

Author: Gorka Navarrete,David R. Mandel

Publisher: Frontiers Media SA

ISBN: 288919745X

Category:

Page: N.A

View: 6784

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.
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Bayes' Rule with Python

A Tutorial Introduction to Bayesian Analysis

Author: James V. Stone

Publisher: Jim Stone

ISBN: 9780993367939

Category: Bayesian statistical decision theory

Page: 176

View: 1097

Discovered by an 18th century mathematician and preacher, Bayes' rule is a cornerstone of modern probability theory. In this richly illustrated book, a range of accessible examples is used to show how Bayes' rule is actually a natural consequence of common sense reasoning. Bayes' rule is then derived using intuitive graphical representations of probability, and Bayesian analysis is applied to parameter estimation. The tutorial style of writing, combined with a comprehensive glossary, makes this an ideal primer for novices who wish to become familiar with the basic principles of Bayesian analysis. Note that this book includes Python (3.0) code snippets, which reproduce key numerical results and diagrams.
Posted in Bayesian statistical decision theory

Perception as Bayesian Inference

Author: David C. Knill,Whitman Richards

Publisher: Cambridge University Press

ISBN: 9780521461092

Category: Computers

Page: 516

View: 9451

This 1996 book describes an exciting theoretical paradigm for visual perception based on experimental and computational insights.
Posted in Computers

An Introduction to Natural Computation

Author: Dana H. Ballard

Publisher: MIT Press

ISBN: 9780262522588

Category: Computers

Page: 307

View: 7218

"This is a wonderful book that brings together in one place the modern view of computation as found in nature. It is well written and has something for everyone from the undergraduate to the advanced researcher." -- Terrence J. Sejnowski, Howard Hughes Medical Institute at The Salk Institute for Biological Studies, La Jolla, California It is now clear that the brain is unlikely to be understood without recourse to computational theories. The theme of An "Introduction to Natural Computation" is that ideas from diverse areas such as neuroscience, information theory, and optimization theory have recently been extended in ways that make them useful for describing the brain's programs. This book provides a comprehensive introduction to the computational material that forms the underpinnings of the currently evolving set of brain models. It stresses the broad spectrum of learning models--ranging from neural network learning through reinforcement learning to genetic learning--and situates the various models in their appropriate neural context. To write about models of the brain before the brain is fully understood is a delicate matter. Very detailed models of the neural circuitry risk losing track of the task the brain is trying to solve. At the other extreme, models that represent cognitive constructs can be so abstract that they lose all relationship to neurobiology. An "Introduction to Natural Computation" takes the middle ground and stresses the computational task while staying near the neurobiology. The material is accessible to advanced undergraduates as well as beginning graduate students. CONTENTS: 1. Introduction Part I "Core Concepts" 2. Fitness 3. Programs 4. Data 5. Dynamics 6. Optimization Part II "Memories" 7. Content Addressible Memories 8. Supervised Learning 9. Unsupervised Learning Part III "Programs" 10. Markov Models 11. Reinforcement Learning Part IV "Systems" 12. Genetic Algorithms
Posted in Computers

Decision Theory

Principles and Approaches

Author: Giovanni Parmigiani,Lurdes Inoue

Publisher: John Wiley & Sons

ISBN: 047074667X

Category: Mathematics

Page: 402

View: 924

Decision theory provides a formal framework for making logical choices in the face of uncertainty. Given a set of alternatives, a set of consequences, and a correspondence between those sets, decision theory offers conceptually simple procedures for choice. This book presents an overview of the fundamental concepts and outcomes of rational decision making under uncertainty, highlighting the implications for statistical practice. The authors have developed a series of self contained chapters focusing on bridging the gaps between the different fields that have contributed to rational decision making and presenting ideas in a unified framework and notation while respecting and highlighting the different and sometimes conflicting perspectives. This book: Provides a rich collection of techniques and procedures. Discusses the foundational aspects and modern day practice. Links foundations to practical applications in biostatistics, computer science, engineering and economics. Presents different perspectives and controversies to encourage readers to form their own opinion of decision making and statistics. Decision Theory is fundamental to all scientific disciplines, including biostatistics, computer science, economics and engineering. Anyone interested in the whys and wherefores of statistical science will find much to enjoy in this book.
Posted in Mathematics

Die Berechnung der Zukunft

Warum die meisten Prognosen falsch sind und manche trotzdem zutreffen - Der New York Times Bestseller

Author: Nate Silver

Publisher: Heyne Verlag

ISBN: 3641112702

Category: Business & Economics

Page: 656

View: 5052

Zuverlässige Vorhersagen sind doch möglich! Nate Silver ist der heimliche Gewinner der amerikanischen Präsidentschaftswahlen 2012: ein begnadeter Statistiker, als »Prognose-Popstar« und »Wundernerd« weltberühmt geworden. Er hat die Wahlergebnisse aller 50 amerikanischen Bundesstaaten absolut exakt vorausgesagt – doch damit nicht genug: Jetzt zeigt Nate Silver, wie seine Prognosen in Zukunft Terroranschläge, Umweltkatastrophen und Finanzkrisen verhindern sollen. Gelingt ihm die Abschaffung des Zufalls? Warum werden Wettervorhersagen immer besser, während die Terrorattacken vom 11.09.2001 niemand kommen sah? Warum erkennen Ökonomen eine globale Finanzkrise nicht einmal dann, wenn diese bereits begonnen hat? Das Problem ist nicht der Mangel an Informationen, sondern dass wir die verfügbaren Daten nicht richtig deuten. Zuverlässige Prognosen aber würden uns helfen, Zufälle und Ungewissheiten abzuwehren und unser Schicksal selbst zu bestimmen. Nate Silver zeigt, dass und wie das geht. Erstmals wendet er seine Wahrscheinlichkeitsrechnung nicht nur auf Wahlprognosen an, sondern auf die großen Probleme unserer Zeit: die Finanzmärkte, Ratingagenturen, Epidemien, Erdbeben, den Klimawandel, den Terrorismus. In all diesen Fällen gibt es zahlreiche Prognosen von Experten, die er überprüft – und erklärt, warum sie meist falsch sind. Gleichzeitig schildert er, wie es gelingen kann, im Rauschen der Daten die wesentlichen Informationen herauszufiltern. Ein unterhaltsamer und spannender Augenöffner!
Posted in Business & Economics

Principles of Applied Statistics

An Integrated Approach Using MINITAB and Excel

Author: Michael C. Fleming,Joseph G. Nellis

Publisher: Cengage Learning EMEA

ISBN: 9781861525864

Category: Business & Economics

Page: 474

View: 6668

This guide examines the principles of statistical data, probability, regression and correlation analysis, forecasting and time-series analysis, emphasizing their practical applications.
Posted in Business & Economics

Encyclopedia of Perception

Author: E. Bruce Goldstein

Publisher: SAGE

ISBN: 1412940818

Category: Psychology

Page: 1180

View: 6343

Because of the ease with which we perceive, many people see perception as something that "just happens." However, even seemingly simple perceptual experiences involve complex underlying mechanisms, which are often hidden from our conscious experience. These mechanisms are being investigated by researchers and theorists in fields such as psychology, cognitive science, neuroscience, computer science, and philosophy. A few examples of the questions posed by these investigations are, What do infants perceive? How does perception develop? What do perceptual disorders reveal about normal functioning? How can information from one sense, such as hearing, be affected by information from another sense, such as vision? How is the information from all of our senses combined to result in our perception of a coherent environment? What are some practical outcomes of basic research in perception? These are just a few of the questions this encyclopedia will consider, as it presents a comprehensive overview of the field of perception for students, researchers, and professionals in psychology, the cognitive sciences, neuroscience, and related medical disciplines such as neurology and ophthalmology.
Posted in Psychology