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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…
Aug 26,2025
Making Bayesian Statistics Accessible to Everyone – Edition 8: Noninformative Priors for Location and Scale Parameters
Introduction In this eighth edition of our Bayesian series, we delve into a refined class of noninformative priors, specifically for location and scale parameters. This builds directly upon our previous edition, where we introduced the…
Aug 26,2025
Introduction to Statistical Decision Theory – Edition 10: Minimaxity, Admissibility, and the Geometry of Statistical Decisions
1. Minimax Rules: Example Consider nonrandomized decision rules only. Randomized minimax rules will be discussed later. $\begin{array}{c|cccccc} & d_1 & d_2 & d_3 & d_4 & d_5 & d_6 \ \hline R(\theta_1, d_i) & 17…
