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An Introduction to Applied Bayesian Methods is a concise yet comprehensive guide designed to help readers master the fundamentals of Bayesian statistical modeling. This book bridges the gap between theory and application, offering practical insights into Bayesian methods through real-world examples and hands-on coding exercises. Covering topics such as regression, hierarchical models, and meta-analysis, it equips readers with the tools to implement Bayesian approaches using R and Stan, making it an essential resource for modern data analysis. As data complexity grows, traditional frequentist approaches often fall short in flexibility and interpretability. This book, on the other hand, provides a probabilistically consistent framework that adapts seamlessly to complex problems. It emphasizes practical application, showing how Bayesian models can handle variability, uncertainty, and predictive challenges in ways that are both intuitive and robust. Whether you're analyzing textbook prices, soil moisture, or multivariate data, this book demonstrates the power of Bayesian thinking. Supplemental Nimble code is also available online, offering additional flexibility for readers. This book is ideal for advanced undergraduate students, researchers, and professionals in statistics and related fields. If you have a basic understanding of Bayesian principles and want to deepen your knowledge with practical examples, this book is for you. It's also a valuable resource for educators teaching applied Bayesian methods. Key Features: - Comprehensive coverage of Bayesian regression and hierarchical models. - Practical examples using R and Stan code. - Step-by-step guidance on model comparison and predictive analysis. - Includes detailed visual representations for interpreting complex data. - Clear explanations of posterior distributions and uncertainty visualization. - Accessible for both beginners and experienced practitioners.
Gilbert W. Fellingham is a Professor of Statistics at Brigham Young University. His primary research interests are Bayesian and Nonparametric Bayesian methods applied to health and human performance. He is currently serving as editor-in-chief of the Journal of Quantitative Analysis in Sports. Scott A. Baldwin is a professor of clinical psychology at Brigham Young University. His research focuses on methodological, psychometric, and statistical challenges in psychotherapy research and the social science generally. He teaches course on psychotherapy, research methods, statistics, and measurement.
Preface I Getting Our Bearings 1 Why Bayes 2 A Brief Look Under the Hood 3 Appropriate Chains and Inference II Building Our Base 4 Two Independent Groups 5 Cell Means Model 6 Linear Regression 7 Multiple Regression 8 Cell Means Redux 9 Regression with Binary Data III Getting Specific 10 Multiple Sources of Variability 11 Censored Data 12 Meta-analysis 13 Multivariate Data 14 Miscellaneous Problems Bibliography Index
