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: 2970

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: 7538

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 Theorem Examples

Author: Scott Hartshorn

Publisher: Lulu Press, Inc

ISBN: 1329854128

Category: Education

Page: N.A

View: 3040

Bayes theorem describes the probability of an event based on other information that might be relevant. Essentially, you are estimating a probability, but then updating that estimate based on other things that you know. This book is designed to give you an intuitive understanding of how to use Bayes Theorem. It starts with the definition of what Bayes Theorem is, but the focus of the book is on providing examples that you can follow and duplicate. Most of the examples are calculated in Excel, which is useful for updating probability if you have dozens or hundreds of data points to roll in.
Posted in Education

Bayes Theorem Examples

The Beginner's Guide to Understanding Bayes Theorem and It's Applications

Author: Logan Styles

Publisher: Createspace Independent Publishing Platform

ISBN: 9781535194594

Category:

Page: 100

View: 8631

Discover how to use Bayes' Theorem for real world applications like weather prediction, criminal investigation, blackjack games, and countless others! Picture this... You've been feeling sick for a couple days. You have a job interview on Thursday. Today is Monday, and you want to make sure you're healthy by Thursday...but you can't afford the time or cost of seeing a doctor before then. What are the odds of being up and running by Thursday? Do they get better if you've just started a new health kick? Or do they stay the same? Or perhaps... ...you notice your good ol' dog Spike walking clumsily and think he may be going blind. However you can't take him to a vet immediately...but you still want to know what the odds are that something's wrong with his eyes. So how do you determine this? These questions and countless others can be better answered when you apply Bayes' Theorem. To simplify it, Bayes' Theorem is the method by which you use to determine the probability of an event based on conditions that may be related to an event. So if you want to determine if your dog is sick and you know his breed is a golden retriever...well you could possibly use that information to assess the likely odds of him being sick! In this guide you'll see example after example of Bayes' Theorem being put into practice. You'll also see how each conclusion is arrived at with summation notation and basic equations. BUT...the purpose of this book isn't just to throw equations at you. It's to help you get an intuitive feel for the probability of an outcome without having to plug in all the numbers. I made sure this book wasn't filled with too much jargon or advanced notation. In fact, this book can be used if...1. You're just a lay person interested in learning how to "predict" the chances of events and gain deeper insight to the world around us2. You're a student who needs to learn about Bayes' Theorem quickly and easily3. You're a teacher or educator looking to advance or brush up on your existing knowledge of Bayes' Theorem I encourage you to download 'Bayes Theorem' so you can make more informed approximations of how events will play out. Plus, when you download "Bayes Theorem", you'll also discover: How to solve unobvious questions How to do your own genetic testing (find out if you're more prone to certain types of ailments) Why a smoker and non-smoker may have equal chances of developing chronic bronchitis How companies can use Bayes' Theorem to manipulate and spew propaganda What the chances are of someone becoming addicted to pills How to determine if a suspected criminal is more likely innocent or guilty The proper mathematical equations and notation to use-and guided explanations of each So download 'Bayes Theorem' today and enhance your statistical knowledge on the world and how things work
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The Signal and the Noise

Why So Many Predictions Fail, But Some Don't

Author: Nate Silver

Publisher: Penguin

ISBN: 0143125087

Category: Business & Economics

Page: 534

View: 9495

The founder of FiveThirtyEight.com challenges myths about predictions in subjects ranging from the financial market and weather to sports and politics, profiling the world of prediction to explain how readers can distinguish true signals from hype, in a report that also reveals the sources and societal costs of wrongful predictions.
Posted in Business & Economics

Bayes' Rule With R

A Tutorial Introduction to Bayesian Analysis

Author: James V Stone

Publisher: N.A

ISBN: 9780993367946

Category: Mathematics

Page: 186

View: 3711

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: 4116

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

Probability Theory

The Logic of Science

Author: E. T. Jaynes

Publisher: Cambridge University Press

ISBN: 1139435167

Category: Science

Page: N.A

View: 989

The standard rules of probability can be interpreted as uniquely valid principles in logic. In this book, E. T. Jaynes dispels the imaginary distinction between 'probability theory' and 'statistical inference', leaving a logical unity and simplicity, which provides greater technical power and flexibility in applications. This book goes beyond the conventional mathematics of probability theory, viewing the subject in a wider context. New results are discussed, along with applications of probability theory to a wide variety of problems in physics, mathematics, economics, chemistry and biology. It contains many exercises and problems, and is suitable for use as a textbook on graduate level courses involving data analysis. The material is aimed at readers who are already familiar with applied mathematics at an advanced undergraduate level or higher. The book will be of interest to scientists working in any area where inference from incomplete information is necessary.
Posted in Science

Data Mining Algorithms

Explained Using R

Author: Pawel Cichosz

Publisher: John Wiley & Sons

ISBN: 111833258X

Category: Computers

Page: 720

View: 3886

"This book narrows down the scope of data mining by adopting a heavily modeling-oriented perspective"--
Posted in Computers

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: 6707

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

A Student’s Guide to Bayesian Statistics

Author: Ben Lambert

Publisher: SAGE

ISBN: 1526418266

Category: Social Science

Page: 520

View: 4209

Supported by a wealth of learning features, exercises, and visual elements as well as online video tutorials and interactive simulations, this book is the first student-focused introduction to Bayesian statistics. Without sacrificing technical integrity for the sake of simplicity, the author draws upon accessible, student-friendly language to provide approachable instruction perfectly aimed at statistics and Bayesian newcomers. Through a logical structure that introduces and builds upon key concepts in a gradual way and slowly acclimatizes students to using R and Stan software, the book covers: An introduction to probability and Bayesian inference Understanding Bayes' rule Nuts and bolts of Bayesian analytic methods Computational Bayes and real-world Bayesian analysis Regression analysis and hierarchical methods This unique guide will help students develop the statistical confidence and skills to put the Bayesian formula into practice, from the basic concepts of statistical inference to complex applications of analyses.
Posted in Social Science

Bayesian Methods for Hackers

Probabilistic Programming and Bayesian Inference

Author: Cameron Davidson-Pilon

Publisher: Addison-Wesley Professional

ISBN: 0133902927

Category: Computers

Page: 256

View: 9870

Master Bayesian Inference through Practical Examples and Computation–Without Advanced Mathematical Analysis Bayesian methods of inference are deeply natural and extremely powerful. However, most discussions of Bayesian inference rely on intensely complex mathematical analyses and artificial examples, making it inaccessible to anyone without a strong mathematical background. Now, though, Cameron Davidson-Pilon introduces Bayesian inference from a computational perspective, bridging theory to practice–freeing you to get results using computing power. Bayesian Methods for Hackers illuminates Bayesian inference through probabilistic programming with the powerful PyMC language and the closely related Python tools NumPy, SciPy, and Matplotlib. Using this approach, you can reach effective solutions in small increments, without extensive mathematical intervention. Davidson-Pilon begins by introducing the concepts underlying Bayesian inference, comparing it with other techniques and guiding you through building and training your first Bayesian model. Next, he introduces PyMC through a series of detailed examples and intuitive explanations that have been refined after extensive user feedback. You’ll learn how to use the Markov Chain Monte Carlo algorithm, choose appropriate sample sizes and priors, work with loss functions, and apply Bayesian inference in domains ranging from finance to marketing. Once you’ve mastered these techniques, you’ll constantly turn to this guide for the working PyMC code you need to jumpstart future projects. Coverage includes • Learning the Bayesian “state of mind” and its practical implications • Understanding how computers perform Bayesian inference • Using the PyMC Python library to program Bayesian analyses • Building and debugging models with PyMC • Testing your model’s “goodness of fit” • Opening the “black box” of the Markov Chain Monte Carlo algorithm to see how and why it works • Leveraging the power of the “Law of Large Numbers” • Mastering key concepts, such as clustering, convergence, autocorrelation, and thinning • Using loss functions to measure an estimate’s weaknesses based on your goals and desired outcomes • Selecting appropriate priors and understanding how their influence changes with dataset size • Overcoming the “exploration versus exploitation” dilemma: deciding when “pretty good” is good enough • Using Bayesian inference to improve A/B testing • Solving data science problems when only small amounts of data are available Cameron Davidson-Pilon has worked in many areas of applied mathematics, from the evolutionary dynamics of genes and diseases to stochastic modeling of financial prices. His contributions to the open source community include lifelines, an implementation of survival analysis in Python. Educated at the University of Waterloo and at the Independent University of Moscow, he currently works with the online commerce leader Shopify.
Posted in Computers

Bayesian Spectrum Analysis and Parameter Estimation

Author: G. Larry Bretthorst

Publisher: Springer Science & Business Media

ISBN: 146849399X

Category: Mathematics

Page: 209

View: 1353

This work is essentially an extensive revision of my Ph.D. dissertation, [1J. It 1S primarily a research document on the application of probability theory to the parameter estimation problem. The people who will be interested in this material are physicists, economists, and engineers who have to deal with data on a daily basis; consequently, we have included a great deal of introductory and tutorial material. Any person with the equivalent of the mathematics background required for the graduate level study of physics should be able to follow the material contained in this book, though not without eIfort. From the time the dissertation was written until now (approximately one year) our understanding of the parameter estimation problem has changed extensively. We have tried to incorporate what we have learned into this book. I am indebted to a number of people who have aided me in preparing this docu ment: Dr. C. Ray Smith, Steve Finney, Juana Sunchez, Matthew Self, and Dr. Pat Gibbons who acted as readers and editors. In addition, I must extend my deepest thanks to Dr. Joseph Ackerman for his support during the time this manuscript was being prepared.
Posted in Mathematics

Thoughtful Machine Learning

A Test-Driven Approach

Author: Matthew Kirk

Publisher: "O'Reilly Media, Inc."

ISBN: 1449374107

Category: Computers

Page: 236

View: 5857

Learn how to apply test-driven development (TDD) to machine-learning algorithms—and catch mistakes that could sink your analysis. In this practical guide, author Matthew Kirk takes you through the principles of TDD and machine learning, and shows you how to apply TDD to several machine-learning algorithms, including Naive Bayesian classifiers and Neural Networks. Machine-learning algorithms often have tests baked in, but they can’t account for human errors in coding. Rather than blindly rely on machine-learning results as many researchers have, you can mitigate the risk of errors with TDD and write clean, stable machine-learning code. If you’re familiar with Ruby 2.1, you’re ready to start. Apply TDD to write and run tests before you start coding Learn the best uses and tradeoffs of eight machine learning algorithms Use real-world examples to test each algorithm through engaging, hands-on exercises Understand the similarities between TDD and the scientific method for validating solutions Be aware of the risks of machine learning, such as underfitting and overfitting data Explore techniques for improving your machine-learning models or data extraction
Posted in Computers

Bayes Theorem: Bayes Theorem Examples

Bayes Theorem Made Easy for Beginners with Step by Step Guidelines to Solve Any Problem

Author: K. A. Muhith

Publisher: Createspace Independent Publishing Platform

ISBN: 9781540675132

Category:

Page: 114

View: 666

Bayes Theorem: Bayes Theorem Examples: A Step by Step Guide For Beginners This book describes Bayes' Theorem in the simplest way possible in layman's language. This book does not contain complex formulas, jargon and hard-to-understand mathematical processes. Some unique examples like US presidential election (Trump vs Hilary!), picnic day, job interview, accident eyewitness reliability, breathalyzer test has been described and solved elaborately in step by step manner in this booklet. After going through this book, you will have a better understanding on what Bayes' Theorem is, when & where you can apply it and how it can help you deduce the most logical conclusions. From Amazon search results to dating, from spam filtering from email to search & rescue, from finding who might win the election to finding a missing plane - Bayes' has been used in real life scenario for many years. Bayes' Theorem is part of syllabus for science and business students. It is one the most basic theorems of statistics. But most teaching techniques of this theorem is too much analytical. Very little intuitive and visual aids is used to demonstrate this theorem in practice. This makes it very hard to grasp the core concept of Bayes' theorem and understand the applicability. This guide addresses this issue and introduces some visual examples and step by step guidelines to solve real life problems. There easy to follow steps will help you apply Bayes' theorem quickly in real life.
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