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Aug 26,2025
Making Bayesian Statistics Accessible to Everyone – Edition 3: Understanding the Beta-Binomial Distribution
Introduction This third edition is presented as a focused interlude to formally introduce an essential building block of Bayesian modeling: the Beta-Binomial distribution. This distribution is not only elegant from a mathematical perspective, but also…
Aug 26,2025
Introduction to Statistical Decision Theory- Edition 5: Optimal Decision Rules
Content Main topics: Admissible decision rules Bayes decision rules Minimax decision rules Context: Parameter estimation 1. Admissibility: The Idea In statistical decision theory, we aim to choose good decision rules from all possible ones. Let…
Aug 26,2025
Making Bayesian Statistics Accessible to Everyone – Edition 4: Summarizing and Interpreting Bayesian Results
Introduction In Edition 2, we explored motivating examples that helped solidify key Bayesian ideas, from credible intervals to beta-binomial modeling and clinical trial analysis. Edition 3 examined the mathematical foundations of the Beta-Binomial distribution, a…
Aug 26,2025
Introduction to Statistical Decision Theory- Edition 6: Bayes Decision Rules
1. From Classical to Bayesian Decision Making In earlier editions, we defined: Statistical decision problems Point estimation, hypothesis testing, confidence intervals Loss functions and risk functions Concepts of admissibility, dominance, and optimality In Edition 6,…
Aug 26,2025
Making Bayesian Statistics Accessible to Everyone – Edition 5: A Bayesian Use Case – Monitoring Vaccine Efficacy in a Phase 3 Trial
Summary Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and the resulting disease, COVID-19, have afflicted tens of millions of people globally. The urgent need for safe and effective vaccines led to a large-scale phase 3…
Aug 26,2025
Introduction to Statistical Decision Theory- Edition 7- Application: Bayesian Estimation under Weighted Quadratic Loss
Introduction In the previous edition, we explored how decision theory provides rules for estimating unknown parameters using loss functions and Bayesian rules. Now, we go one step further by introducing weighted quadratic loss and how…
Aug 26,2025
Making Bayesian Statistics Accessible to Everyone – Edition 6: Conjugate Prior Distributions – Mathematical Foundations and Applications
Introduction In this sixth edition, we take a deeper look into the structure of Bayesian models by introducing the concept of conjugate prior distributions. These are prior distributions that lead to posterior distributions in the…
Aug 26,2025
Introduction to Statistical Decision Theory – Edition 8: Application: Bayes Rule under Weighted Loss in the Normal-Normal Model
Overview In this edition, we study the Bayes rule under a weighted squared loss for the Normal-Normal model. We will: Derive the posterior distribution for a single observation. Show that the Bayes rule has a…
Aug 26,2025
Making Bayesian Statistics Accessible to Everyone – Edition 7: Noninformative Priors and the Jeffreys Rule
Introduction In Edition 7, we address a foundational yet subtle aspect of Bayesian inference: noninformative priors. Also referred to as “vague,” “flat,” or “reference” priors, they are used when we want our prior beliefs to…
Aug 26,2025
Introduction to Statistical Decision Theory – Edition 9: Understanding Minimax Rules: Making the Best of the Worst
Introduction: What’s at Stake? Imagine you have to make a decision, but you don’t know exactly what the true state of the world is. You’re stuck in a game against uncertainty, and you’d like to…
