Bayesian Data Analysis

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This book serves three key roles: as an introductory text on Bayesian inference from first principles, a graduate-level guide on current Bayesian modeling and computational approaches, and a practical handbook for applied statistics users and researchers. While the early sections are introductory, the content is not elementary and requires a foundation in basic probability, statistics, elementary calculus, and linear algebra. Chapter 1 provides a review of probability notation and outlines the assumed knowledge. The book emphasizes practical applications, recognizing that readers should have experience in probability, statistics, and linear algebra with a strong computational focus. Merely presenting an introductory text would leave readers lacking guidance for real-world applications, especially where Bayesian methods align with traditional non-Bayesian analyses. Conversely, introducing advanced methods without foundational concepts would be inadequate. The text includes a variety of worked examples from real applications to illustrate current Bayesian methodologies. To maintain clarity, bibliographic notes are provided at the end of each chapter, along with a comprehensive list of references at the conclusion of the book.