## Course syllabus

MVE155 / MSG200 Statistical inference (7.5 hp) 2021

Course is offered by the department of Mathematical Sciences

Serik Sagitov

### Course purpose

"Statistical Inference" is a second course in mathematical statistics suitable for students with different backgrounds. A main prerequisite is an introductory course in probability and statistics. The course gives a deeper understanding of some traditional topics in mathematical statistics such as methods based on likelihood, aspects of experimental design, non-parametric testing, analysis of variance, introduction to Bayesian inference, chi-squared tests, multiple regression.

Install Rstudio

Step 1: install R from http://ftp.acc.umu.se/mirror/CRAN/

No previous knowledge of programming is required.

### Schedule

We meet online via Zoom Link Passcode 899022

Recorded Zoom sessions can be found under the option "Modules".

 Date, usual time 13.15-15.00 Description of sessions Chapters in Compendium Mon 18/01 Lecture 1: Random sampling  Slides1.pdf Chapters 1-3 Tue 19/01 Exercise 1: 3.6.1, 3.6.2, R session QQplot.R Wed 20/01 Lecture 2: Stratified samples Slides2.pdf. Parametric models  Slides3.pdf Chapters 3-4 Mon 25/01 Exercise 2: 3.6.6, 3.6.7, 3.6.8, 4.7.1, R solution of 3.6.7 Tue 26/01 Lecture 3: Maximum likelihood  Slides4.pdf. R session Multinomial and Chi2 .R Chapter 4 Wed 27/01 Exercise 3:  4.7.3, 4.7.5, 4.7.6, 4.7.7 Fri 29/01 Lecture 4: Hypothesis testing Slides5.pdf, Slides6.pdf Chapter 5 Mon 01/02 Exercise 4: 5.8.1, 5.8.4, 5.8.6, 5.8.7, 5.8.10 Tue 02/02 Lecture 5: Bayesian inference Slides7.pdf. R session Bayes.R Chapter 6 Wed 03/02 Exercise 5: 5.8.2, 5.8.9, 5.8.12, 6.5.4 Fri 05/02 Lecture 6: Bayesian inference  Slides8.pdf Chapter 6 Mon 08/02 Exercise 6: 6.5.1, 6.5.2, 6.5.3, 6.5.5, 6.5.6 Tue 09/02 Lecture 7: Empirical distribution Slides9.pdf. R session Summarising Data.R Chapter 7 Wed 10/02 Exercise 7: 7.7.1, 7.7.2, 7.7.3, 7.7.4, 7.7.5, 7.7.6. R session ExercisesCh7.R Fri 12/02 Lecture 8: Comparing two populations Slides10.pdf, Slides11.pdf Chapter 8 Mon 15/02 Exercise 8: 8.6.2, 8.6.5, 8.6.9, 8.6.11 Tue 16/02 Lecture 9: ANOVA1  Slides11.pdf, Slides12.pdf Chapter 8-9 Wed 17/02 Exercise 9: R session t-test and ANOVA.R Fri 19/02 Lecture 10: ANOVA2 Slides13.pdf Chapter 9 Mon 22/02 Exercise 10: 9.8.1, 9.8.2, 9.8.3, 9.8.4, 9.8.7 Tue 23/02 Lecture 11: Nonparametric tests Slides14.pdf. R session Nonparametric tests.R Chapter 9-10 Wed 24/02 Exercise 11: 8.6.3, 8.6.4, 8.6.7, 8.6.8, 9.8.5, 9.8.6, Mon 01/03 Lecture 12: Categorical data Slides15.pdf. R session Chi-square test.R Chapter 10 Tue 02/03 Exercise 12: 10.5.3, 10.5.6, 10.5.7, 10.5.9. An example of a final exam Wed 03/03 Lecture 13: Simple linear regression Slides16.pdf Chapter 11 Fri 05/03 Exercise 13: 11.6.5, 11.6.6. R session Regression.R Mon 08/03 Lecture 14: Multiple regression Slides17.pdf Chapter 11 Tue 09/03 Exercise 14: 11.6.3, 11.6.4, 11.6.7, 14.1.1, 14.1.14, 14.1.21, 14.1.9 Chapter 14 Tue 16/03, 14.00-18.00 Exam 1 (register before 28.02.2021) Wed 09/06, 8.30-12.30 Exam 2 (register before ) Tue 17/08, 14.00-18.00 Exam 3 (register before )

### Course literature

The course is build around the Compendium - click and download. The compendium may undergo minor updates - on the first page you will see when it was last updated.

Recommended additional textbook: Mathematical statistics and data analysis, 3rd edition (2nd edition is also OK), by John Rice (Cremona).

### Learning objectives and syllabus

Learning objectives:

- summarize multiple sample data in a meaningful and informative way,

- recognize several basic types of statistical problems corresponding to various sampling designs,

- estimate relevant parameters and perform appropriate statistical tests for multiple sample data sets.

Link to the syllabus on Studieportalen: Study plan

### Examination form

The grading of the course is based on a written examination. Preparing for the final exam, check Section 12.1 of the Compendium to see the list of the topics that may be addressed by the final exam questions.

Several old exams with solutions are given in the module "Old exams".

Maximal number of points for the final exam is 30. Passing limits

• CTH students: 12 points for '3', 18 points for '4', 24 points for '5'
• GU students: 12 points for 'G', 20 points for 'VG'

Date Details Due