# MSF100/MVE326, Statistical Inference Principles, Spring 18

## Latest news

Welcome to the course! The schedule for the course can be found in TimeEdit.

7/12: The first meeting to fix the schedule of the course is on Monday, January 15, 8:00 in MVH:11.

15/1: The course schedule is fixed, see TimeEdit and below. Exercises will be due every Thursday before the class and will be presented by the students during that class.

15/1: The student representatives of the course are: Oskar Allerbo (PhD students), Erik Håkansson (GU), Joel Sjögren (Chalmers)

12/2: Problem 4 on Assignment 4 was updated. The missing square was added. Please check the new version! Sorry for any inconvenience this might have caused and thank you to Oskar for spotting the typo!

10/4: The final grades should now be visible to all students. Please find below the exam with solution.

## Teachers

Course coordinator: Annika Lang

## Course literature

Casella/Berger: Statistical Inference (2nd edition)

Hogg/McKean/Craig: Introduction to Mathematical Statistics (Person New International Edition 7e)

Jacod/Protter: Probability Essentials

Migon/Gamerman/Louzada: Statistical Inference: An Integrated Approach (2nd edition)

Wasserman: All of Statistics

## Program

#### Lectures

Day
Sections Contents
Mon 15/1
8 - 10
MVH11
e.g. [JP]
Introduction to random variables and expectations
Wed 17/1
8 - 10
MVF31
[CB] 5.1, 5.2
Introduction to variance, independence, random samples, statistics
Thur 18/1
15 - 17
MVF31
[CB] 5.2, 5.4, 6.2
[HMKC] 7.2
[MGL] 2.5
Sample mean, sample variance, exponential families, order statistics, sample median, distribution of order statistics, sufficient statistics
Mon 22/1
10 - 12
ML15
[CB] 6.2
[HMKC] 7.2
[MGL] 2.5
Factorization Theorem (Fisher-Neyman-Halmos-Savage), minimal sufficeint statistics, Lehmann-Scheffé Theorem
Wed 24/1
8 - 10
MVF31
[CB] 6.2, 6.3
[HMKC] 7.8, 7.9
[MGL] 2.5
Ancillary and complete statistics, Basu's Theorem, likelihood principle
Thur 25/1
15 - 17
MVF31

Discussion of Assignment 1
Mon 29/1
10 - 12
ML15
[CB]  7.2.1, 7.2.2
[HMKC] 6.1
[MGL] 4.3.1, 4.3.3
Point estimation: method of moments, maximum likelihood estimators
Wed 31/1
8 - 10
MVF31
[CB] 7.2.3, 7.2.4
[HMKC] 11.2.1, 11.2.2, 6.6
[MGL] 4.2, 5.2.2
Point estimation: Bayes estimators, EM algorithm
Thur 1/2
15 - 17
MVF31
[CB] 7.3.1, 7.3.2
[HMKC] 7.1
[MGL] 4.5
Discussion of Assignment 2, mean squared errors, best unbiased estimators
Mon 5/2
10 - 12
ML15
[CB] 7.3.2, 7.3.3
[HMKC] 6.2, 7.3
[MGL] 4.5
Cramér-Rao inequality, Rao-Blackwell Theorem
Wed 7/2
8 - 10
MVF31
[CB] 7.3.3, 7.3.4, 8.1, 8.2.1
[HMKC] 6.2, 7.1, 6.3
[MGL] 4.5, 4.1, 4.5, 6.1, 6.2
Properties of best unbiased estimators, loss and risk functions, introduction to hypothesis testing, likelihood ratio tests
Thur 8/2
15 - 17
MVF31
[CB] 8.2.1, 8.2.2
[HMKC] 6.3
[MGL] 6.2, 11.2.4
Discussion of Assignment 3, LRT, Bayesian tests
Mon 12/2
10 - 12
ML15
[CB] 8.2.3, 8.3.1, 8.3.2
[HMKC] 8.1
[MGL] 6.2
Union-intersection/intersection-union tests, errors of Type I and II, UMP tests, statement Neyman-Pearson lemma
Wed 14/2
8 - 10
MVF31
[CB] 8.3.2
[HMKC] 8.1
[MGL] 6.2.1, 6.2.2
Proof Neyman-Pearson lemma, monotone likelihood ratios, Karlin-Rubin theorem
Thur 15/2
15 - 17
MVF31
[CB] 8.3.4
[HMKC] 4.6
[MGL] 6.2
Discussion of Assignment 4, p-values
Mon 19/2
10 - 12
ML15
[CB] 9.1, 9.2.1, 9.2.2
[HMKC] 4.2
[MGL] 4.6
Introduction to interval estimation, test inversion, pivoting
Wed 21/2
8 - 10
MVF31
[CB] 9.2.2, 9.2.3, 9.2.4
[HMKC] 4.2
[MGL] 4.6
Pivoting, Bayesian set estimates
Thur 22/2
15 - 17
MVF31
[CB] 9.2.4, 9.3.1
[HMKC] 4.2
[MGL] 4.6
Discussion of Assignment 5, Bayesian set estimates, evaluation of interval estimates
Mon 26/2
10 - 12
ML15
[CB] 9.3.1, 9.3.2, 10
[HMKC] 4.2, 5
[MGL] 4.6, 5.3
Evaluation of interval estimators, size and coverage probabilities, test-related optimality, asymptotic evaluations
Wed 28/2
8 - 10
MVF31
[CB] 10
[HMKC] 5
[MGL] 5.3
Asymptotic evaluations
Thur 1/3
15 - 17
MVF31

Discussion of Assignment 6, conclusions

#### Homework due

Day
Exercises
Thur 25/1
Assignment 1
Thur 1/2
Assignment 2
Thur 8/2
Assignment 3
Thur 15/2
Assignment 4
Thur 22/2
Assignment 5
Thur 1/3 Assignment 6

## Computer labs

#### Reference literature:

Learning MATLAB, Tobin A. Driscoll ISBN: 978-0-898716-83-2 (The book is published by SIAM).

## Course requirements

The learning goals of the course can be found in the course plan.

## Assignments

Weekly assignments are given and due every Thursday. Students present the solutions in weekly exercise classes on Thursday and are requested to be able to present solutions for 75% of the exercises. The assignments consist of a combinations of theoretical exercises and programming tasks which can be implemented in the preferred programming language.

The hand-in of assignments works as follows:

• Send an email to annika.lang@chalmers.se no later than 14:30 on Thursday, where you give a list of solved exercises (on average not less than 75%).
• Come to the class on Thursday and be ready to present all exercises that you listed in the email at the blackboard. Bad presentations will not count as "presentation" and you will have to hand in a full corrected solution within a week that is distributed to all participants (else the problem will be deleted from your record of solved exercises and no model solution will be given).
• Two successful presentations are mandatory to pass.

## Examination

Besides the assignments (2.5 hp) a written 4 hour exam (5 hp) has to be passed on Saturday, 17/3 in TBA. To pass the exam 50% of the points are required.

## Examination procedures

In Chalmers Student Portal you can read about when exams are given and what rules apply on exams at Chalmers. In addition to that, there is a schedule when exams are given for courses at University of Gothenburg.

Before the exam, it is important that you sign up for the examination. If you study at Chalmers, you will do this by the Chalmers Student Portal, and if you study at University of Gothenburg, you sign up via GU's Student Portal, where you also can read about what rules apply to examination at University of Gothenburg.

At the exam, you should be able to show valid identification.