| APTS: Statistical Inference |
| Lecturer: | Simon Shaw; s.shaw at bath.ac.uk |
Lecture Notes: pdf.
Slides covering all material: pdf.
Material covered:
| Lecture 1 (16 Dec 19): | §2 Principles for Statistical Inference: reasoning about inferences, idea of the evidence function, the principle of indifference, mixture experiment, (strong) likelihood principle, Birnbaum's Theorem. |
| Lecture slides: pdf. Lecture notes: p18 (start of chapter) - p22 (prior to Section 2.5). | |
| Lecture 2 (17 Dec 19): | Weak and strong sufficiency principles, relationship of sufficiency to Birnbaum's theorem, stopping rule principle and implied by the (strong) likelihood principle, relationship of the Bayesian approach to the (strong) likelihood principle. Note: Section 2.7 was omitted. |
| Lecture slides: pdf. Lecture notes: p22 (start of Section 2.5) - p27 (paragraph after equation (2.13)). | |
| Lecture 3 (17 Dec 19): | Classical methods typically violate the (strong) likelihood principle. §3 Statistical Decision Theory: loss function, ingredients of a statistical decision problem, Bayes rule and Bayes risk, Bayes decision rule and risk of the sampling procedure, classical risk. |
| Lecture slides: pdf. Lecture notes: p27 (paragraph after equation (2.13)) - p35 (after Definition 15). | |
| Lecture 4 (18 Dec 19): | Admissible rules, admissibility of Bayes rules, Wald's Complete Class Theorem, loss functions for point estimation, set estimation and the trade-off between containment and volume, level set property for Bayes rules, hypothesis tests. |
| Lecture slides: pdf. Lecture notes: p35 (after Definition 15) - p39 (end of Chapter 3). | |
| Lecture 5 (19 Dec 19): | §4 Confidence sets and p-values: confidence procedure and set, constructing confidence procedures, likelihood ratio test, duality of acceptance regions and confidence sets, level set property for the likelihood. |
| Lecture slides: pdf. Lecture notes: p40 (start of Chapter 4) - p44 (after Definition 21). | |
| Lecture 6 (19 Dec 19): | Constructing a confidence procedure with the level set property, the linear model and exact confidence procedures with the level set property, Wilks confidence procedures, p-value, super-uniform random variable, significance procedures and duality with confidence procedures. |
| Lecture slides: pdf. Lecture notes: p44 (after Definition 21) - p50 (end of Section 4.4). | |
| Lecture 7 (20 Dec 19): | Families of significance procedures, computing p-values via simulation using exchangeability, concluding remarks. Note: Section 4.6 largely omitted. |
| Lecture slides: pdf. Lecture notes: p50 (start of Section 4.5) - p55 (end of course). |