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Table of Contents

Phase I: Foundational Probability & Theory

Chapter 1: Bayes’ Theorem & Probability Foundations
Chapter 2: The Great Debate: Frequentist vs. Bayesian Statistics
Chapter 3: Conjugate Priors & Posterior Distributions
Chapter 4: Bayesian Estimators and Credible Intervals
Chapter 5: Loss Functions and Decision Theory

Phase II: Computational Methodology & Algorithmic Design

Chapter 6: Bayesian Hypothesis Testing & Model Comparison
Chapter 7: Markov Chain Monte Carlo (MCMC) – Part I
Chapter 8: MCMC – Part II (Advanced Topics)
Chapter 9: Variational Inference

Phase III: Advanced Applications & Generalized Linear Architectural Frameworks

Chapter 10: Bayesian Linear and Logistic Regression
Chapter 11: Hierarchical (Multilevel) Bayesian Models
Chapter 12: Model Diagnostics and Posterior Predictive Checks
Chapter 13: Bayesian Model Averaging
Chapter 14: Prior Elicitation and Sensitivity Analysis
Chapter 15: Applications – Econometrics, Finance, and Machine Learning