## Messages

21.08: Chapter 1. Probability and distributions.

22.08: Chapter 1 and 2: Distributions, combinatorics, transformations and expectation. Slides week 34

28.08: Momentgenerating function, differentiation under an Integral sign. Chapter 2.4. Chapter 3.1-3.2. Commmon families of distributions

29.08: Chapter 3.2-3. Negative binomial, gamma, exponential and Chi-square distributions.

04.09: No lecture

05.09: Beta distribution and Chapter 3.4 Exponential family of distributions. Slides week 35

11.09: Chapter 3.4 Exponential family of distributions. Chapter 3.5. Location and scale families. Slides week 36

12.09: Chapter 3.6 Inequalities. Chapter 4.2 and 4.3 Bivariate distributions

18.09: Chapter 4.4: Hierarchical models and mixture distributions. Slides week 37

19.09: Chapter 4.5-4.7: Covariance and correlations, inequalities.

25.09: Chapter 5.1-2: Random samples Chapter 5.3: Nomally Distributed random sample, Chisquare distribution and t-distribution. Slides week 38

26.09: Chapter 5.3 and 5.5: F-distribution and convergence in probability and distribution.

Report from Reference group meeting September 30.

02.10: Chapter 5.5.1 and 5.5.3: Convergence in probability and distribution. Slides week 39

03.10: Chapter 5.5.4 and 6.2; The Delta Method and Sufficiency.

09.10: Chapter 6.2.1 and 6.2.2 Sufficient estimators. Slides week 40

10.10: Chapter 6.2.2 Sufficiency and exponential class. Minimal sufficiency.

16.10: Chapter 6.2.2 7.2.1-7.2.2. Minimal sufficieny and Maximum likelihood. Slides week 41

17.10: Chapter 7.2.2-7.2.3: Maximum likelihood, invariance and Bayes estimator.

23.10: Chapter 7.2.2 and 7.2.3 Bayes estimator, MSE. Bayes and the normal distribution in details

Slides week 42

24.10: Chapter 7.3.2 Cramer-Rao Inequality and Equality.

30.10: Chapter 7.3.2 and 7.3.3. Cramer-Rao. Sufficiency and Unbiasedness. Slides week 43. Cramer-Rao in the multiparameter case

31.10: Chapter 7.3.3 Sufficiency and Unbiasedness. Chapter 6.2.4. Complete statistic.

Report from Reference group meeting October 29.

06.11: Chapter 8.2.1 Likelihood ratio test.Chapter 8.3. Methods of Evaluating tests. Slides week 44

07.11: Chapter 8.3.2 Most powerful tests, Neymann-Pearson. Chapter 9.1, 9.2.1 Confidence intervals. Methods of finding confidence intervals.

13.11: Chapter 9.2.1 and 9.2.2: Methods of finding confidence intervals. Inverting the LRT and Pivotal quantities Slides week 45

14.11: Chapter 9.2.3 and 9.2.4: Pivoting the cdf and Bayesian Interval

20.11: Chapter 9.2.4: Bayesian Intervals. Chapter 10.1.1-10.1.2. Point estimation and efficiency. Slides week 46

21.11: Chapter 10.3.1: Asymptotic distribution of the LRT. Repetition.

Report from Reference group meeting November 25.

## Lectures

Wednesdays: 14.15-16.00 in room MA24.

Thursdays: 14:15-16:00 in room MA24.

## Exercises

Fridays 09:15-10:00 (**NB! changed**) in room MA24. First time 06.09. Three of the exercises will be compulsory in order to be allowed to take the exam. The rest are not, but they are also extemely important for the exam.

Exercise 1, 06.09: 2.33ac, 2.35, 2.38, 3.28abd, 3.39. lf

Exercise 2, 13.09: Exercise 2 lf

Exercise 3, 19.09: 3,46, 3.47 (hard), 4.1, 4.4, 4.10, 4.34. lf

Exercise 4: 27.09: 4.15, 4.30, 4.31, 4.32, 4.35, 4.36, 4.58. **This exercise is compulsory and must be handed
in before 15.00 October 1. Use preferably Blackboard for handing in the exercise. In case of problems you may send
in by email to Jacopo Paglia.** lf

Exercise 5: 04.10: 5.6, 5.17, 5.31, 5.35 lf

Exercise 6: 11.10: 5.36, 5.43a), 5.44, 6.1.lf

Exercise 7: Exercise 7
lf

Exercise 8: Exercise 8 **This exercise is compulsory and must be handed
in before 15.00 October 29. Use preferably Blackboard for handing in the exercise. In case of problems you may send
in by email to Jacopo Paglia.** lf

Exercise 9: Exercise 9. lf

Exercise 10: Exercise 10. lf

Exercise 11: Exercise 11 **This exercise is compulsory and must be handed
in before 15.00 November 19. Use preferably Blackboard for handing in the exercise. In case of problems you may send
in by email to Jacopo Paglia.** lf

Exercise 10: Exercise 12. lf

## Teacher

John Tyssedal, room 1132, SII. Email: John [dot] tyssedal [at] ntnu [dot] no

Meeting hour Fridays 9.00 - 10.00.

## Teaching assistant

Jacopo Paglia, room 1001, SII. Email: jacopo [dot] paglia [at] ntnu [dot] no

## Reference group

Elen Ekeberg Klippen elenek [at] stud [dot] ntnu [dot] no

Eliane Huygens Olsen elianeho [at] stud [dot] ntnu [dot] no

Leonardo Constantini leonarco [at] stud [dot] ntnu [dot] no

## Curriculum

The curriculum is defined to be all that is covered in lectures and exercises, as described on the course homepage under "Lecture plan and progress" and "Exercises".

The following list gives references to the planned topics covered from the course book: **Statistical Inference by George Casella and Roger Berger** (Second Edition)

*Chapter 1: Probability theory.* Assumed known

*Chapter 2: Transformations and expectations.* 2.1 (assumed known); 2.2-2.4

*Chapter 3: Common families of distributions.* 3.1-3.3 (assumed known); 3.4, 3.5, 3.6.1

*Chapter 4: Multiple random variables.* 4.1-4.6 (4.5 only partly); 4.7 (only Cauchy-Schwarz and Jensen's inequality)

*Chapter 5: Properties of a random sample.* 5.1-5.3 (not all in detail),5.5.1, 5.5.3, 5.5.4.

*Chapter 6: Principles of data reduction.* 6.1, 6.2.1, 6.2.2, Def. 6.2.21, Examples 6.22.22-23, Theorem 6.2.25

*Chapter 7: Point estimation.* 7.1, 7.2.1, 7.2.2, 7.2.3, 7.3.1 (except from "In certain situationsâ€¦" on p. 333), 7.3.2, 7.3.3 (from beginning to Example 7.3.18, then from top of page 347 and rest of section 7.3.3; Theorem 7.5.1.

*Chapter 8: Hypothesis testing.* 8.1, 8.2.1, 8.3.1 (except page 387), 8.3.2 until Def. 8.3.16 (only part a in Theorem 8.3.12).

*Chapter 9: Interval estimation.* 9.1, 9.2

*Chapter 10: Asymptotic evaluations.* 10.1.1, 10.1.2, 10.1.3, 10.3.1 to theorem 10.3.3, Score statistic on page 494.

## Exam

It will be a written exam on December 19. at 9.00. It lasts for four hours. You are allowed to bring with you:

Tabeller og formler i statistikk

NTNU certified calculator

Personal, handwritten, stamped yellow sheet, A5-format. You get the sheet in the Department office, 7. floor

The exam text will contain a collections of results from the text-book as given here

Earlier exams with solutions can be found here:earlier exams

The exam 2017 with suggested solution

The exam 2018 with suggested solution

The exam 2019 with suggested solution

The curriculum should make you able to solve the problems in most of the earlier exams, but you will meet questions about ARE or Square Loss function in a Bayesian setting in some of them. That is not covered by our curriculum, and you will not meet such questions on the exam.

Meeting hours before the exam in my offfice

Monday 16. December 12-14

Tuesday 17. December 13-15

Wednesday 18. December 13-15