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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
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
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
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…
Aug 26,2025
Introduction to Statistical Decision Theory – Edition 11: A Medical Application
Introduction This edition focuses on a practical application of statistical decision theory in a medical context. We explore how a doctor can apply a randomized decision rule to minimize potential loss when diagnosing a disease…
Aug 26,2025
Introduction to Statistical Decision Theory – Edition 12: Application to Classification Decisions with Finite Hypotheses
Bayesian Classification with Finite Hypotheses In this lesson, we study how to make good classification decisions using Bayesian Decision Theory. The goal is to decide which group or class an observation belongs to, based on…
