Bayesian Programming (Chapman & Hall/ Crc: Machine Learning & Pattern Recognition)

__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. 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. Front Cover 1 Dedication 6 Contents 8 Foreword 16 Preface 18 Chapter 1: Introduction 20 Part I: Bayesian Programming Principles 34 Chapter 2: Basic Concepts 36 Chapter 3: Incompleteness and Uncertainty 54 Chapter 4: Description = Specification + Identification 66 Chapter 5: The Importance of Conditional Independence 84 Chapter 6: Bayesian Program = Description + Question 94 Part II: Bayesian Programming Cookbook 110 Chapter 7: Information Fusion 112 Chapter 8: Bayesian Programming with Coherence Variables 140 Chapter 9: Bayesian Programming Subroutines 172 Chapter 10: Bayesian Programming Conditional Statement 190 Chapter 11: Bayesian Programming Iteration 202 Part III: Bayesian Programming Formalism and Algorithms 216 Chapter 12: Bayesian Programming Formalism 218 Chapter 13: Bayesian Models Revisited 228 Chapter 14: Bayesian Inference Algorithms Revisited 266 Chapter 15: Bayesian Learning Revisited 300 Part IV: Frequently Asked Questions — Frequently Argued Matters 328 Chapter 16: Frequently Asked Questions and Frequently Argued Matters 330 Chapter 17: Glossary 350 Bibliography 360 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 emphasizes probability as an alternative to Boolean logic, covering new methods to build probabilistic programs for real-world applications. The book encourages readers to explore emerging areas and develop new programming languages and hardware architectures. A Python package is available on a supplementary website. Pierre Bessière ... [et Al.]. A Chapman & Hall Book. Includes Bibliographical References (pages 341-358).