Bayesian Methods for Hackers

Probabilistic Programming and Bayesian Inference

Author: Cameron Davidson-Pilon

Publisher: Addison-Wesley Professional

ISBN: 0133902927

Category: Computers

Page: 256

View: 6466

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.
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Bayesian Methods for Hackers

Probabilistic Programming and Bayesian Methods

Author: Cameron Davidson-Pilon

Publisher: Addison-Wesley Professional

ISBN: 9780133902839

Category: Computers

Page: 320

View: 9288

Master Bayesian Inference through Practical Examples and Computation Not 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 vs. exploitation dilemma: deciding when pretty good is good enough Using Bayesian inference to improve A/B testing Solving data science problems that rely on mountains of data"
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Bayesian Programming

Author: Pierre Bessiere,Emmanuel Mazer,Juan Manuel Ahuactzin,Kamel Mekhnacha

Publisher: CRC Press

ISBN: 1439880336

Category: Business & Economics

Page: 380

View: 2701

Probability as an Alternative to Boolean Logic While logic is the mathematical foundation of rational reasoning and the fundamental principle of computing, it is restricted to problems where information is both complete and certain. However, many real-world problems, from financial investments to email filtering, are incomplete or uncertain in nature. Probability theory and Bayesian computing together provide an alternative framework to deal with incomplete and uncertain data. Decision-Making Tools and Methods for Incomplete and Uncertain Data Emphasizing probability as an alternative to Boolean logic, Bayesian Programming covers new methods to build probabilistic programs for real-world applications. Written by the team who designed and implemented an efficient probabilistic inference engine to interpret Bayesian programs, the book offers many Python examples that are also available on a supplementary website together with an interpreter that allows readers to experiment with this new approach to programming. Principles and Modeling Only requiring a basic foundation in mathematics, the first two parts of the book present a new methodology for building subjective probabilistic models. The authors introduce the principles of Bayesian programming and discuss good practices for probabilistic modeling. Numerous simple examples highlight the application of Bayesian modeling in different fields. Formalism and Algorithms The third part synthesizes existing work on Bayesian inference algorithms since an efficient Bayesian inference engine is needed to automate the probabilistic calculus in Bayesian programs. Many bibliographic references are included for readers who would like more details on the formalism of Bayesian programming, the main probabilistic models, general purpose algorithms for Bayesian inference, and learning problems. FAQs Along with a glossary, the fourth part contains answers to frequently asked questions. The authors compare Bayesian programming and possibility theories, discuss the computational complexity of Bayesian inference, cover the irreducibility of incompleteness, and address the subjectivist versus objectivist epistemology of probability. The First Steps toward a Bayesian Computer A new modeling methodology, new inference algorithms, new programming languages, and new hardware are all needed to create a complete Bayesian computing framework. Focusing on the methodology and algorithms, this book describes the first steps toward reaching that goal. It encourages readers to explore emerging areas, such as bio-inspired computing, and develop new programming languages and hardware architectures.
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Bayesian Analysis with Python

Author: Osvaldo Martin

Publisher: Packt Publishing Ltd

ISBN: 1785889850

Category: Computers

Page: 282

View: 2227

Unleash the power and flexibility of the Bayesian framework About This Book Simplify the Bayes process for solving complex statistical problems using Python; Tutorial guide that will take the you through the journey of Bayesian analysis with the help of sample problems and practice exercises; Learn how and when to use Bayesian analysis in your applications with this guide. Who This Book Is For Students, researchers and data scientists who wish to learn Bayesian data analysis with Python and implement probabilistic models in their day to day projects. Programming experience with Python is essential. No previous statistical knowledge is assumed. What You Will Learn Understand the essentials Bayesian concepts from a practical point of view Learn how to build probabilistic models using the Python library PyMC3 Acquire the skills to sanity-check your models and modify them if necessary Add structure to your models and get the advantages of hierarchical models Find out how different models can be used to answer different data analysis questions When in doubt, learn to choose between alternative models. Predict continuous target outcomes using regression analysis or assign classes using logistic and softmax regression. Learn how to think probabilistically and unleash the power and flexibility of the Bayesian framework In Detail The purpose of this book is to teach the main concepts of Bayesian data analysis. We will learn how to effectively use PyMC3, a Python library for probabilistic programming, to perform Bayesian parameter estimation, to check models and validate them. This book begins presenting the key concepts of the Bayesian framework and the main advantages of this approach from a practical point of view. Moving on, we will explore the power and flexibility of generalized linear models and how to adapt them to a wide array of problems, including regression and classification. We will also look into mixture models and clustering data, and we will finish with advanced topics like non-parametrics models and Gaussian processes. With the help of Python and PyMC3 you will learn to implement, check and expand Bayesian models to solve data analysis problems. Style and approach Bayes algorithms are widely used in statistics, machine learning, artificial intelligence, and data mining. This will be a practical guide allowing the readers to use Bayesian methods for statistical modelling and analysis using Python.
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Applied Bayesian Hierarchical Methods

Author: Peter D. Congdon

Publisher: CRC Press

ISBN: 9781584887218

Category: Mathematics

Page: 604

View: 3776

The use of Markov chain Monte Carlo (MCMC) methods for estimating hierarchical models involves complex data structures and is often described as a revolutionary development. An intermediate-level treatment of Bayesian hierarchical models and their applications, Applied Bayesian Hierarchical Methods demonstrates the advantages of a Bayesian approach to data sets involving inferences for collections of related units or variables and in methods where parameters can be treated as random collections. Emphasizing computational issues, the book provides examples of the following application settings: meta-analysis, data structured in space or time, multilevel and longitudinal data, multivariate data, nonlinear regression, and survival time data. For the worked examples, the text mainly employs the WinBUGS package, allowing readers to explore alternative likelihood assumptions, regression structures, and assumptions on prior densities. It also incorporates BayesX code, which is particularly useful in nonlinear regression. To demonstrate MCMC sampling from first principles, the author includes worked examples using the R package. Through illustrative data analysis and attention to statistical computing, this book focuses on the practical implementation of Bayesian hierarchical methods. It also discusses several issues that arise when applying Bayesian techniques in hierarchical and random effects models.
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Applied Multivariate Analysis

Using Bayesian and Frequentist Methods of Inference, Second Edition

Author: S. James Press

Publisher: Courier Corporation

ISBN: 0486442365

Category: Mathematics

Page: 671

View: 8538

Includes practical elements of matrix theory, continuous multivariate distributions and basic multivariate statistics in the normal distribution; regression and the analysis of variance; factor analysis and latent structure analysis; canonical correlations; stable portfolio analysis; classifications and discrimination models; control in the multivariate linear model; and structuring multivariate populations. 1982 edition.
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Building Probabilistic Graphical Models with Python

Author: Kiran R Karkera

Publisher: Packt Publishing Ltd

ISBN: 1783289015

Category: Computers

Page: 172

View: 5184

This is a short, practical guide that allows data scientists to understand the concepts of Graphical models and enables them to try them out using small Python code snippets, without being too mathematically complicated. If you are a data scientist who knows about machine learning and want to enhance your knowledge of graphical models, such as Bayes network, in order to use them to solve real-world problems using Python libraries, this book is for you.This book is intended for those who have some Python and machine learning experience, or are exploring the machine learning field.
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Learning from Data

Concepts, Theory, and Methods

Author: Vladimir Cherkassky,Filip M. Mulier

Publisher: John Wiley & Sons

ISBN: 9780470140512

Category: Computers

Page: 624

View: 6437

An interdisciplinary framework for learning methodologies—covering statistics, neural networks, and fuzzy logic, this book provides a unified treatment of the principles and methods for learning dependencies from data. It establishes a general conceptual framework in which various learning methods from statistics, neural networks, and fuzzy logic can be applied—showing that a few fundamental principles underlie most new methods being proposed today in statistics, engineering, and computer science. Complete with over one hundred illustrations, case studies, and examples making this an invaluable text.
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Think Bayes

Author: Allen Downey

Publisher: "O'Reilly Media, Inc."

ISBN: 1491945443

Category: Computers

Page: 210

View: 7528

If you know how to program with Python and also know a little about probability, you’re ready to tackle Bayesian statistics. With this book, you'll learn how to solve statistical problems with Python code instead of mathematical notation, and use discrete probability distributions instead of continuous mathematics. Once you get the math out of the way, the Bayesian fundamentals will become clearer, and you’ll begin to apply these techniques to real-world problems. Bayesian statistical methods are becoming more common and more important, but not many resources are available to help beginners. Based on undergraduate classes taught by author Allen Downey, this book’s computational approach helps you get a solid start. Use your existing programming skills to learn and understand Bayesian statistics Work with problems involving estimation, prediction, decision analysis, evidence, and hypothesis testing Get started with simple examples, using coins, M&Ms, Dungeons & Dragons dice, paintball, and hockey Learn computational methods for solving real-world problems, such as interpreting SAT scores, simulating kidney tumors, and modeling the human microbiome.
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Practical Probabilistic Programming

Author: Avi Pfeffer

Publisher: N.A

ISBN: 9781617292330

Category: Computers

Page: 456

View: 9568

Summary Practical Probabilistic Programming introduces the working programmer to probabilistic programming. In it, you'll learn how to use the PP paradigm to model application domains and then express those probabilistic models in code. Although PP can seem abstract, in this book you'll immediately work on practical examples, like using the Figaro language to build a spam filter and applying Bayesian and Markov networks, to diagnose computer system data problems and recover digital images. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the Technology The data you accumulate about your customers, products, and website users can help you not only to interpret your past, it can also help you predict your future! Probabilistic programming uses code to draw probabilistic inferences from data. By applying specialized algorithms, your programs assign degrees of probability to conclusions. This means you can forecast future events like sales trends, computer system failures, experimental outcomes, and many other critical concerns. About the Book Practical Probabilistic Programming introduces the working programmer to probabilistic programming. In this book, you’ll immediately work on practical examples like building a spam filter, diagnosing computer system data problems, and recovering digital images. You’ll discover probabilistic inference, where algorithms help make extended predictions about issues like social media usage. Along the way, you’ll learn to use functional-style programming for text analysis, object-oriented models to predict social phenomena like the spread of tweets, and open universe models to gauge real-life social media usage. The book also has chapters on how probabilistic models can help in decision making and modeling of dynamic systems. What's Inside Introduction to probabilistic modeling Writing probabilistic programs in Figaro Building Bayesian networks Predicting product lifecycles Decision-making algorithms About the Reader This book assumes no prior exposure to probabilistic programming. Knowledge of Scala is helpful. About the Author Avi Pfeffer is the principal developer of the Figaro language for probabilistic programming. Table of Contents PART 1 INTRODUCING PROBABILISTIC PROGRAMMING AND FIGARO Probabilistic programming in a nutshell A quick Figaro tutorial Creating a probabilistic programming application PART 2 WRITING PROBABILISTIC PROGRAMS Probabilistic models and probabilistic programs Modeling dependencies with Bayesian and Markov networks Using Scala and Figaro collections to build up models Object-oriented probabilistic modeling Modeling dynamic systems PART 3 INFERENCE The three rules of probabilistic inference Factored inference algorithms Sampling algorithms Solving other inference tasks Dynamic reasoning and parameter learning
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Doing Bayesian Data Analysis

A Tutorial Introduction with R

Author: John Kruschke

Publisher: Academic Press

ISBN: 9780123814869

Category: Mathematics

Page: 672

View: 303

There is an explosion of interest in Bayesian statistics, primarily because recently created computational methods have finally made Bayesian analysis tractable and accessible to a wide audience. Doing Bayesian Data Analysis, A Tutorial Introduction with R and BUGS, is for first year graduate students or advanced undergraduates and provides an accessible approach, as all mathematics is explained intuitively and with concrete examples. It assumes only algebra and ‘rusty’ calculus. Unlike other textbooks, this book begins with the basics, including essential concepts of probability and random sampling. The book gradually climbs all the way to advanced hierarchical modeling methods for realistic data. The text provides complete examples with the R programming language and BUGS software (both freeware), and begins with basic programming examples, working up gradually to complete programs for complex analyses and presentation graphics. These templates can be easily adapted for a large variety of students and their own research needs.The textbook bridges the students from their undergraduate training into modern Bayesian methods. Accessible, including the basics of essential concepts of probability and random sampling Examples with R programming language and BUGS software Comprehensive coverage of all scenarios addressed by non-bayesian textbooks- t-tests, analysis of variance (ANOVA) and comparisons in ANOVA, multiple regression, and chi-square (contingency table analysis). Coverage of experiment planning R and BUGS computer programming code on website Exercises have explicit purposes and guidelines for accomplishment
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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: 3810

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.
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A Student’s Guide to Bayesian Statistics

Author: Ben Lambert

Publisher: SAGE

ISBN: 1526418266

Category: Social Science

Page: 520

View: 4061

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.
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Perceptual Learning

Author: Manfred Fahle,Tomaso Poggio

Publisher: MIT Press

ISBN: 9780262062213

Category: Medical

Page: 455

View: 7748

An overview of the field of perceptual learning -- the study of the permanent changes in cortical structure caused by external stimuli.
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Bayesian Modeling Using WinBUGS

Author: Ioannis Ntzoufras

Publisher: John Wiley & Sons

ISBN: 1118210352

Category: Mathematics

Page: 520

View: 4637

A hands-on introduction to the principles of Bayesian modeling using WinBUGS Bayesian Modeling Using WinBUGS provides an easily accessible introduction to the use of WinBUGS programming techniques in a variety of Bayesian modeling settings. The author provides an accessible treatment of the topic, offering readers a smooth introduction to the principles of Bayesian modeling with detailed guidance on the practical implementation of key principles. The book begins with a basic introduction to Bayesian inference and the WinBUGS software and goes on to cover key topics, including: Markov Chain Monte Carlo algorithms in Bayesian inference Generalized linear models Bayesian hierarchical models Predictive distribution and model checking Bayesian model and variable evaluation Computational notes and screen captures illustrate the use of both WinBUGS as well as R software to apply the discussed techniques. Exercises at the end of each chapter allow readers to test their understanding of the presented concepts and all data sets and code are available on the book's related Web site. Requiring only a working knowledge of probability theory and statistics, Bayesian Modeling Using WinBUGS serves as an excellent book for courses on Bayesian statistics at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners in the fields of statistics, actuarial science, medicine, and the social sciences who use WinBUGS in their everyday work.
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Bayesian Reasoning and Machine Learning

Author: David Barber

Publisher: Cambridge University Press

ISBN: 0521518148

Category: Computers

Page: 697

View: 1321

A practical introduction perfect for final-year undergraduate and graduate students without a solid background in linear algebra and calculus.
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WebGL Programming Guide

Interactive 3D Graphics Programming with WebGL

Author: Kouichi Matsuda,Rodger Lea

Publisher: Addison-Wesley

ISBN: 0133364925

Category: Computers

Page: 552

View: 7112

Using WebGL®, you can create sophisticated interactive 3D graphics inside web browsers, without plug-ins. WebGL makes it possible to build a new generation of 3D web games, user interfaces, and information visualization solutions that will run on any standard web browser, and on PCs, smartphones, tablets, game consoles, or other devices. WebGL Programming Guide will help you get started quickly with interactive WebGL 3D programming, even if you have no prior knowledge of HTML5, JavaScript, 3D graphics, mathematics, or OpenGL. You’ll learn step-by-step, through realistic examples, building your skills as you move from simple to complex solutions for building visually appealing web pages and 3D applications with WebGL. Media, 3D graphics, and WebGL pioneers Dr. Kouichi Matsuda and Dr. Rodger Lea offer easy-to-understand tutorials on key aspects of WebGL, plus 100 downloadable sample programs, each demonstrating a specific WebGL topic. You’ll move from basic techniques such as rendering, animating, and texturing triangles, all the way to advanced techniques such as fogging, shadowing, shader switching, and displaying 3D models generated by Blender or other authoring tools. This book won’t just teach you WebGL best practices, it will give you a library of code to jumpstart your own projects. Coverage includes: • WebGL’s origin, core concepts, features, advantages, and integration with other web standards • How and basic WebGL functions work together to deliver 3D graphics • Shader development with OpenGL ES Shading Language (GLSL ES) • 3D scene drawing: representing user views, controlling space volume, clipping, object creation, and perspective • Achieving greater realism through lighting and hierarchical objects • Advanced techniques: object manipulation, heads-up displays, alpha blending, shader switching, and more • Valuable reference appendixes covering key issues ranging from coordinate systems to matrices and shader loading to web browser settings This is the newest text in the OpenGL Technical Library, Addison-Wesley’s definitive collection of programming guides an reference manuals for OpenGL and its related technologies. The Library enables programmers to gain a practical understanding of OpenGL and the other Khronos application-programming libraries including OpenGL ES and OpenCL. All of the technologies in the OpenGL Technical Library evolve under the auspices of the Khronos Group, the industry consortium guiding the evolution of modern, open-standards media APIs.
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Extreme Programming Explained

Embrace Change

Author: Kent Beck,Cynthia Andres

Publisher: Pearson Education

ISBN: 0321278658

Category: Computers

Page: 189

View: 3782

The first edition of "Extreme Programming Explained" is a classic. It won awards for its then-radical ideas for improving small-team development, such as having developers write automated tests for their own code and having the whole team plan weekly. Much has changed in five years. This completely rewritten second edition expands the scope of XP to teams of any size by suggesting a program of continuous improvement based on: five core values consistent with excellence in software development; eleven principles for putting those values into action; and, thirteen primary and eleven corollary practices to help you push development past its current business and technical limitations. Whether you have a small team that is already closely aligned with your customers or a large team in a gigantic or multinational organization, you will find in these pages a wealth of ideas to challenge, inspire, and encourage you and your team members to substantially improve your software development.
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