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Bayesian Networks

Author: Marco Scutari
Publisher: CRC Press
ISBN: 148222559X
Size: 64.33 MB
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Understand the Foundations of Bayesian Networks—Core Properties and Definitions Explained Bayesian Networks: With Examples in R introduces Bayesian networks using a hands-on approach. Simple yet meaningful examples in R illustrate each step of the modeling process. The examples start from the simplest notions and gradually increase in complexity. The authors also distinguish the probabilistic models from their estimation with data sets. The first three chapters explain the whole process of Bayesian network modeling, from structure learning to parameter learning to inference. These chapters cover discrete Bayesian, Gaussian Bayesian, and hybrid networks, including arbitrary random variables. The book then gives a concise but rigorous treatment of the fundamentals of Bayesian networks and offers an introduction to causal Bayesian networks. It also presents an overview of R and other software packages appropriate for Bayesian networks. The final chapter evaluates two real-world examples: a landmark causal protein signaling network paper and graphical modeling approaches for predicting the composition of different body parts. Suitable for graduate students and non-statisticians, this text provides an introductory overview of Bayesian networks. It gives readers a clear, practical understanding of the general approach and steps involved.

First Complex Systems Digital Campus World E Conference 2015

Author: Paul Bourgine
Publisher: Springer
ISBN: 3319459015
Size: 51.15 MB
Format: PDF, Kindle
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This book contains the proceedings as well as invited papers for the first annual conference of the UNESCO Unitwin Complex System Digital Campus (CSDC), which is an international initiative gathering 120 Universities on four continents, and structured in ten E-Departments. First Complex Systems Digital Campus World E-Conference 2015 features chapters from the latest research results on theoretical questions of complex systems and their experimental domains. The content contained bridges the gap between the individual and the collective within complex systems science and new integrative sciences on topics such as: genes to organisms to ecosystems, atoms to materials to products, and digital media to the Internet. The conference breaks new ground through a dedicated video-conferencing system – a concept at the heart of the international UNESCO UniTwin, embracing scientists from low-income and distant countries. This book promotes an integrated system of research, education, and training. It also aims at contributing to global development by taking into account its social, economic, and cultural dimensions. First Complex Systems Digital Campus World E-Conference 2015 will appeal to students and researchers working in the fields of complex systems, statistical physics, computational intelligence, and biological physics.

Mathematical Theory Of Bayesian Statistics

Author: Sumio Watanabe
Publisher: CRC Press
ISBN: 1315355698
Size: 17.84 MB
Format: PDF
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Mathematical Theory of Bayesian Statistics introduces the mathematical foundation of Bayesian inference which is well-known to be more accurate in many real-world problems than the maximum likelihood method. Recent research has uncovered several mathematical laws in Bayesian statistics, by which both the generalization loss and the marginal likelihood are estimated even if the posterior distribution cannot be approximated by any normal distribution. Features Explains Bayesian inference not subjectively but objectively. Provides a mathematical framework for conventional Bayesian theorems. Introduces and proves new theorems. Cross validation and information criteria of Bayesian statistics are studied from the mathematical point of view. Illustrates applications to several statistical problems, for example, model selection, hyperparameter optimization, and hypothesis tests. This book provides basic introductions for students, researchers, and users of Bayesian statistics, as well as applied mathematicians. Author Sumio Watanabe is a professor of Department of Mathematical and Computing Science at Tokyo Institute of Technology. He studies the relationship between algebraic geometry and mathematical statistics.

Statistical Rethinking

Author: Richard McElreath
Publisher: CRC Press
ISBN: 1315362619
Size: 56.71 MB
Format: PDF, Kindle
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Statistical Rethinking: A Bayesian Course with Examples in R and Stan builds readers’ knowledge of and confidence in statistical modeling. Reflecting the need for even minor programming in today’s model-based statistics, the book pushes readers to perform step-by-step calculations that are usually automated. This unique computational approach ensures that readers understand enough of the details to make reasonable choices and interpretations in their own modeling work. The text presents generalized linear multilevel models from a Bayesian perspective, relying on a simple logical interpretation of Bayesian probability and maximum entropy. It covers from the basics of regression to multilevel models. The author also discusses measurement error, missing data, and Gaussian process models for spatial and network autocorrelation. By using complete R code examples throughout, this book provides a practical foundation for performing statistical inference. Designed for both PhD students and seasoned professionals in the natural and social sciences, it prepares them for more advanced or specialized statistical modeling. Web Resource The book is accompanied by an R package (rethinking) that is available on the author’s website and GitHub. The two core functions (map and map2stan) of this package allow a variety of statistical models to be constructed from standard model formulas.

An Introduction To Generalized Linear Models

Author: Annette J. Dobson
Publisher: CRC Press
ISBN: 1351726218
Size: 12.61 MB
Format: PDF, ePub
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An Introduction to Generalized Linear Models, Fourth Edition provides a cohesive framework for statistical modelling, with an emphasis on numerical and graphical methods. This new edition of a bestseller has been updated with new sections on non-linear associations, strategies for model selection, and a Postface on good statistical practice. Like its predecessor, this edition presents the theoretical background of generalized linear models (GLMs) before focusing on methods for analyzing particular kinds of data. It covers Normal, Poisson, and Binomial distributions; linear regression models; classical estimation and model fitting methods; and frequentist methods of statistical inference. After forming this foundation, the authors explore multiple linear regression, analysis of variance (ANOVA), logistic regression, log-linear models, survival analysis, multilevel modeling, Bayesian models, and Markov chain Monte Carlo (MCMC) methods. Introduces GLMs in a way that enables readers to understand the unifying structure that underpins them Discusses common concepts and principles of advanced GLMs, including nominal and ordinal regression, survival analysis, non-linear associations and longitudinal analysis Connects Bayesian analysis and MCMC methods to fit GLMs Contains numerous examples from business, medicine, engineering, and the social sciences Provides the example code for R, Stata, and WinBUGS to encourage implementation of the methods Offers the data sets and solutions to the exercises online Describes the components of good statistical practice to improve scientific validity and reproducibility of results. Using popular statistical software programs, this concise and accessible text illustrates practical approaches to estimation, model fitting, and model comparisons.

Introduction To Probability With R

Author: Kenneth Baclawski
Publisher: CRC Press
ISBN: 9781420065220
Size: 23.54 MB
Format: PDF
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Based on a popular course taught by the late Gian-Carlo Rota of MIT, with many new topics covered as well, Introduction to Probability with R presents R programs and animations to provide an intuitive yet rigorous understanding of how to model natural phenomena from a probabilistic point of view. Although the R programs are small in length, they are just as sophisticated and powerful as longer programs in other languages. This brevity makes it easy for students to become proficient in R. This calculus-based introduction organizes the material around key themes. One of the most important themes centers on viewing probability as a way to look at the world, helping students think and reason probabilistically. The text also shows how to combine and link stochastic processes to form more complex processes that are better models of natural phenomena. In addition, it presents a unified treatment of transforms, such as Laplace, Fourier, and z; the foundations of fundamental stochastic processes using entropy and information; and an introduction to Markov chains from various viewpoints. Each chapter includes a short biographical note about a contributor to probability theory, exercises, and selected answers. The book has an accompanying website with more information.

Extending The Linear Model With R

Author: Julian J. Faraway
Publisher: CRC Press
ISBN: 9780203492284
Size: 19.68 MB
Format: PDF
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Linear models are central to the practice of statistics and form the foundation of a vast range of statistical methodologies. Julian J. Faraway's critically acclaimed Linear Models with R examined regression and analysis of variance, demonstrated the different methods available, and showed in which situations each one applies. Following in those fo