bayesian ideas and data analysis an introduction for scientists and statisticians chapman hall crc texts in statistical science

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Bayesian Ideas And Data Analysis

Author : Ronald Christensen
ISBN : 9781439803554
Genre : Mathematics
File Size : 26. 79 MB
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Emphasizing the use of WinBUGS and R to analyze real data, Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians presents statistical tools to address scientific questions. It highlights foundational issues in statistics, the importance of making accurate predictions, and the need for scientists and statisticians to collaborate in analyzing data. The WinBUGS code provided offers a convenient platform to model and analyze a wide range of data. The first five chapters of the book contain core material that spans basic Bayesian ideas, calculations, and inference, including modeling one and two sample data from traditional sampling models. The text then covers Monte Carlo methods, such as Markov chain Monte Carlo (MCMC) simulation. After discussing linear structures in regression, it presents binomial regression, normal regression, analysis of variance, and Poisson regression, before extending these methods to handle correlated data. The authors also examine survival analysis and binary diagnostic testing. A complementary chapter on diagnostic testing for continuous outcomes is available on the book’s website. The last chapter on nonparametric inference explores density estimation and flexible regression modeling of mean functions. The appropriate statistical analysis of data involves a collaborative effort between scientists and statisticians. Exemplifying this approach, Bayesian Ideas and Data Analysis focuses on the necessary tools and concepts for modeling and analyzing scientific data. Data sets and codes are provided on a supplemental website.

Discrete Data Analysis With R

Author : Michael Friendly
ISBN : 9781498725859
Genre : Mathematics
File Size : 76. 93 MB
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An Applied Treatment of Modern Graphical Methods for Analyzing Categorical Data Discrete Data Analysis with R: Visualization and Modeling Techniques for Categorical and Count Data presents an applied treatment of modern methods for the analysis of categorical data, both discrete response data and frequency data. It explains how to use graphical methods for exploring data, spotting unusual features, visualizing fitted models, and presenting results. The book is designed for advanced undergraduate and graduate students in the social and health sciences, epidemiology, economics, business, statistics, and biostatistics as well as researchers, methodologists, and consultants who can use the methods with their own data and analyses. Along with describing the necessary statistical theory, the authors illustrate the practical application of the techniques to a large number of substantive problems, including how to organize data, conduct an analysis, produce informative graphs, and evaluate what the graphs reveal about the data. The first part of the book contains introductory material on graphical methods for discrete data, basic R skills, and methods for fitting and visualizing one-way discrete distributions. The second part focuses on simple, traditional nonparametric tests and exploratory methods for visualizing patterns of association in two-way and larger frequency tables. The final part of the text discusses model-based methods for the analysis of discrete data. Web Resource The data sets and R software used, including the authors’ own vcd and vcdExtra packages, are available at http://cran.r-project.org.

Stochastic Modeling And Mathematical Statistics

Author : Francisco J. Samaniego
ISBN : 9781466560475
Genre : Mathematics
File Size : 48. 45 MB
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Provides a Solid Foundation for Statistical Modeling and Inference and Demonstrates Its Breadth of Applicability Stochastic Modeling and Mathematical Statistics: A Text for Statisticians and Quantitative Scientists addresses core issues in post-calculus probability and statistics in a way that is useful for statistics and mathematics majors as well as students in the quantitative sciences. The book’s conversational tone, which provides the mathematical justification behind widely used statistical methods in a reader-friendly manner, and the book’s many examples, tutorials, exercises and problems for solution, together constitute an effective resource that students can read and learn from and instructors can count on as a worthy complement to their lectures. Using classroom-tested approaches that engage students in active learning, the text offers instructors the flexibility to control the mathematical level of their course. It contains the mathematical detail that is expected in a course for "majors" but is written in a way that emphasizes the intuitive content in statistical theory and the way theoretical results are used in practice. More than 1000 exercises and problems at varying levels of difficulty and with a broad range of topical focus give instructors many options in assigning homework and provide students with many problems on which to practice and from which to learn.

Bayesian Methods

Author : Jeff Gill
ISBN : 9781439862490
Genre : Mathematics
File Size : 33. 91 MB
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An Update of the Most Popular Graduate-Level Introductions to Bayesian Statistics for Social Scientists Now that Bayesian modeling has become standard, MCMC is well understood and trusted, and computing power continues to increase, Bayesian Methods: A Social and Behavioral Sciences Approach, Third Edition focuses more on implementation details of the procedures and less on justifying procedures. The expanded examples reflect this updated approach. New to the Third Edition A chapter on Bayesian decision theory, covering Bayesian and frequentist decision theory as well as the connection of empirical Bayes with James–Stein estimation A chapter on the practical implementation of MCMC methods using the BUGS software Greatly expanded chapter on hierarchical models that shows how this area is well suited to the Bayesian paradigm Many new applications from a variety of social science disciplines Double the number of exercises, with 20 now in each chapter Updated BaM package in R, including new datasets, code, and procedures for calling BUGS packages from R This bestselling, highly praised text continues to be suitable for a range of courses, including an introductory course or a computing-centered course. It shows students in the social and behavioral sciences how to use Bayesian methods in practice, preparing them for sophisticated, real-world work in the field.

The Bugs Book

Author : David Lunn
ISBN : 9781466586666
Genre : Mathematics
File Size : 88. 53 MB
Format : PDF
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Bayesian statistical methods have become widely used for data analysis and modelling in recent years, and the BUGS software has become the most popular software for Bayesian analysis worldwide. Authored by the team that originally developed this software, The BUGS Book provides a practical introduction to this program and its use. The text presents complete coverage of all the functionalities of BUGS, including prediction, missing data, model criticism, and prior sensitivity. It also features a large number of worked examples and a wide range of applications from various disciplines. The book introduces regression models, techniques for criticism and comparison, and a wide range of modelling issues before going into the vital area of hierarchical models, one of the most common applications of Bayesian methods. It deals with essentials of modelling without getting bogged down in complexity. The book emphasises model criticism, model comparison, sensitivity analysis to alternative priors, and thoughtful choice of prior distributions—all those aspects of the "art" of modelling that are easily overlooked in more theoretical expositions. More pragmatic than ideological, the authors systematically work through the large range of "tricks" that reveal the real power of the BUGS software, for example, dealing with missing data, censoring, grouped data, prediction, ranking, parameter constraints, and so on. Many of the examples are biostatistical, but they do not require domain knowledge and are generalisable to a wide range of other application areas. Full code and data for examples, exercises, and some solutions can be found on the book’s website.

Statistical Rethinking

Author : Richard McElreath
ISBN : 9781315362618
Genre : Mathematics
File Size : 40. 45 MB
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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.

Bayesian Logical Data Analysis For The Physical Sciences

Author : Phil Gregory
ISBN : 9781139444286
Genre : Mathematics
File Size : 87. 23 MB
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Bayesian inference provides a simple and unified approach to data analysis, allowing experimenters to assign probabilities to competing hypotheses of interest, on the basis of the current state of knowledge. By incorporating relevant prior information, it can sometimes improve model parameter estimates by many orders of magnitude. This book provides a clear exposition of the underlying concepts with many worked examples and problem sets. It also discusses implementation, including an introduction to Markov chain Monte-Carlo integration and linear and nonlinear model fitting. Particularly extensive coverage of spectral analysis (detecting and measuring periodic signals) includes a self-contained introduction to Fourier and discrete Fourier methods. There is a chapter devoted to Bayesian inference with Poisson sampling, and three chapters on frequentist methods help to bridge the gap between the frequentist and Bayesian approaches. Supporting Mathematica® notebooks with solutions to selected problems, additional worked examples, and a Mathematica tutorial are available at www.cambridge.org/9780521150125.

Bayesian Data Analysis Third Edition

Author : Andrew Gelman
ISBN : 9781439840955
Genre : Mathematics
File Size : 51. 38 MB
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Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.

Bayesian Analysis Made Simple

Author : Phil Woodward
ISBN : 9781439839553
Genre : Mathematics
File Size : 75. 6 MB
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Although the popularity of the Bayesian approach to statistics has been growing for years, many still think of it as somewhat esoteric, not focused on practical issues, or generally too difficult to understand. Bayesian Analysis Made Simple is aimed at those who wish to apply Bayesian methods but either are not experts or do not have the time to create WinBUGS code and ancillary files for every analysis they undertake. Accessible to even those who would not routinely use Excel, this book provides a custom-made Excel GUI, immediately useful to those users who want to be able to quickly apply Bayesian methods without being distracted by computing or mathematical issues. From simple NLMs to complex GLMMs and beyond, Bayesian Analysis Made Simple describes how to use Excel for a vast range of Bayesian models in an intuitive manner accessible to the statistically savvy user. Packed with relevant case studies, this book is for any data analyst wishing to apply Bayesian methods to analyze their data, from professional statisticians to statistically aware scientists.

Data Analysis

Author : Devinderjit Sivia
ISBN : 9780191546709
Genre : Mathematics
File Size : 84. 33 MB
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