## Messages

18.08: Chapter 1. Probability and distributions. Lecturenotes 1

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

25.08: Momentgenerating function, differentiation under an Integral sign. Chapter 2.4. Chapter 3.1-3.2. Commmon families of distributions Lecturenotes 3

26.08: Chapter 3.2-3. Negative binomial, gamma, exponential and Chi-square distributions. Lecturenotes 4

01.09: Chapter 3.4. Exponential family of distributions. Chapter 3.5. Location and scale families. Lecturenotes 5. Slides week 35.

02.09: Chapter 3.5. Location and scale families. Chapter 3.6 Inequalities. Chapter 4.2 Multivariate distributions. Lecturenotes 6.

08.09: Chapter 3.6 Chapter 4.2 and 4.3 Bivariate distributions Chapter 4.4: Hierarchical models and mixture distributions. Slides week 36

Lecturenotes 7.

09.09: Chapter 4.5-4.7: Covariance and correlations, inequalities. Lecturenotes 8.

15.09: Jensens inequality, Chapter 5.1-2: Random samples Chapter 5.3: Nomally Distributed random sample, Chisquare distribution. Slides week 37

Lecturenotes 9.

16.09: Chapter 5.3 and 5.5: t-distribution, F-distribution and convergence in probability and distribution. Lecturenotes 10.

22.09: Chapter 5.5.1 and 5.5.3: Convergence in probability and distribution. Slides week 38. Lecturenotes 11.

23.09: Chapter 5.5.3 and 5.5.4: The Central limit theorem and the Delta Method. Lecturenotes 12.

24.09: Referat referansegruppemøte.

29.09: Chapter 5.5.4 and 6.2; The Delta Method and Sufficiency. Lecturenotes 13. Slides week 39.

30.09: Chapter 6.2.1 and 6.2.2 Sufficient estimators and Minimal sufficiency. Lecturenotes 14.

Comments to the first compulsatory exercise

06.10: Chapter 6.2.2. Minimal sufficiency and exponential class. Lecturenotes 15. Slides week 40.

07.10: Chapter 7.2.1-7.2.2. Maximum likelihood and the invariance principle. Lecturenotes 16.

13.10: Chapter 7.2.2 and 7.2.3 Bayes estimator, MSE. Bayes and the normal distribution in details. Lecturenotes 17. Slides week 41.

14.10: Chapter 7.3.2 Cramer-Rao Inequality and Equality. Lecturenotes 18.

20.10: Chapter 7.3.2 and 7.3.3. Cramer-Rao. Sufficiency and Unbiasedness. Cramer-Rao in the multiparameter case. Lecturenotes 19. Slides week 42.

21.10:Chapter 6.2.4. Complete statistic. 7.3.3 Sufficiency and Unbiasedness. Lecturenotes 20.

26.10: Referat 2. referansegruppemøte.

27.10: Chapter 8.1 and 8.2. Hypothesis testing and Likelihood ratio test. Lecturenotes 21. Slides week 43.

28.10: Chapter 8.3. Methods of Evaluating tests. Most powerful tests, Neymann-Pearson. Lecturenotes 22.

**There is now a new heading on this web page, where new information about the exam 2020 will be posted**.

03.11: Chapter 9.2.1 and 9.2.2: Methods of finding confidence intervals. Inverting the LRT. Lecturenotes 23. Slides week 44. Comments to Exercise 8.

04.11: Chapter 9.2.3 and 9.2.4: Pivoting quantities. Pivoting the CDF. Lecturenotes 24.

10.11: Chapter 9.2.3 and 9.2.4: Pivoting the cdf and Bayesian Interval. Lecturenotes 25. Slides week 45.

11.11: Chapter 9.2.4: Bayesian Intervals. Chapter 10.1.1-10.1.2. Point estimation and efficiency. Lecturenotes 26.

A very clear majority voted for physical lectures the last week. Also considering that the infection rate is still rather low, there will be physical lectures the last week too.

17.11: Chapter 10.1.1-10.1.2. Point estimation and efficiency.Chapter 10.3.1: Asymptotic distribution of the LRT. Lecturenotes 27. Slides week 46.

18.11: Repetition. Slides frå repetisjonen.

19.11: Referat 3. referansegruppemøte.

21.12: The exam is corrected. There were many excellent answers and many of you would have received a good mark on a normal exam. I am impressed that you have prepared that well given the circumstances.

## Lectures

Tuesdays: 14.15-16.00 in room K 5.

Wednesdays: 14:15-16:00 in room K 5.

## Exercises

Tuesdays 16:15-17:00 in room K5. First time 01.09. 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, 01.09: 2.33ac, 2.35, 2.38, 3.20, 3.23. lf

Exercise 2, 08.09: Exercise 2. lf

Exercise 3, 15.09: 3,46, 3.47 (hard), 4.1, 4.4, 4.10, 4.34. lf

Exercise 4: 22.09: 4.15, 4.30, 4.31, 4.32, 4.35, 4.36, 4.58. lf **This exercise is compulsory and must be handed
in before 15.00 September 25. Use preferably Blackboard for handing in the exercise. In case of problems you may send
in by email to Silius Vandeskog**

Exercise 5: 29.09: 5.6, 5.17, 5.31, 5.35. lf

Exercise 6: 06.10: 5.36, 5.43a), 5.44, 6.1. lf

Exercise 7: 13.10: Exercise 7. lf

Exercise 8: 20.10: Exercise 8. lf **This exercise is compulsory and must be handed
in before 15.00 October 23. Use preferably Blackboard for handing in the exercise. In case of problems you may send
in by email to Silius Vandeskog**.

Exercise 9 27.10: Exercise 9. lf

Exercise 10 03.11: Exercise 10. lf

Exercise 11 10.11: Exercise 11. lf **This exercise is compulsory and must be handed
in before 15.00 November 13. Use preferably Blackboard for handing in the exercise. In case of problems you may send
in by email to Silius Vandeskog.**

Exercise 12 17.11: Exercise 12. lf

## Lecturer

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

## Teaching assistant

Silius Mortensønn Vandeskog, room 1126, SII. Email: silius [dot] m [dot] vandeskog [at] ntnu [dot] no

## Reference group

Karina Lilleborge. Email: karinali [at] stud [dot] ntnu [dot] no

Emma Skarstein. Email:emmaska [at] stud [dot] ntnu [dot] no

Håkon Noren. Email: haakno [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 "Messages" 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 situations…" 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.

## About Exam 2020

To all students in TMA4295

Rector has decided that all written school exams will be changed to home exams. In addition the faculty has decided that all oral exams need to be digital and not physical. The results of the poll about the alternatives; "oral exam with marks"/"written home exam with pass or fail" ended up about 60/40 in favour of written home exam. Considering all the effort needed to also have sensor(s) for an oral exam we have therefore decided that the exam will be a written home exam with pass/fail.

The exam will be December 14, 9-13. Thirty minutes will be added to the exam for scanning and uploading of elements.
The exam problems will have the same form as for an ordinary written exam. All printed and hand-written support material is allowed. Answers to the problems shall be written by hand either on paper or ipad for thereafter to be uploaded to Inspera. Mobiles or other devices can be used to scan paper to pdf files. It is an advantage to try out taking pictures of a document and save it as a pdf on your computer in advance. Some guidelines can be found here:

Oppskrift på lagring til PDF

Meir informasjon om digital vurdering .

*Meeting hours before the exam*

The meetings will be digital.

Wednesday December 9: 13.00-15.00

https://NTNU.zoom.us/j/96303399526?pwd=M0M0YlJaMTFrdDdrU3JwWEJOdXFBZz09

Meeting ID: 963 0339 9526

Passcode: 185073

Thursday December 10: 13.00-15.00

https://NTNU.zoom.us/j/91948952787?pwd=QllyY2lTVG91TDg3bTVQd3BwSCtaQT09

Meeting ID: 919 4895 2787

Passcode: 986889

Friday December 11: 13.00-15.00

https://NTNU.zoom.us/j/99135163162?pwd=TTU4RTZlb1RFNzZZSWRVNnJ1dkFXZz09

Meeting ID: 991 3516 3162

Passcode: 377955