1. SylabUZ
2. Wydział Matematyki, Informatyki i Ekonometrii
3. semestr zimowy 2022/2023
4. Computer science and econometrics - drugiego stopnia z tyt. magistra
5. Multivariate Analysis

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Multivariate Analysis - opis przedmiotu

Cel przedmiotu

Aim of the course is to familiarize students with statistical methods applied for analyzing multivariate data.

Wymagania wstępne

Zapisz zmiany

Passed lectures on: linear algebra, probability theory, mathematical statistics.

Zakres tematyczny

Lecture

1. Random vectors and its probability distributions. Multivariate normal distribution.          (4 hours)
2. Introduction to point estimation in multivariate models. (4 hours)
3. Fundamental sample distribution for multivariate normal model. (4 hours)
4. Hotelling’s T^2 distribution and its applications. (6 hours)
5. Principal components. (4 hours)
6. Analysis of canonical correlation. (4 hours)
7. Discriminant analysis. (4 hours)

               Class

1. Some elements form linear algebra used in multivariate statistical inferences. (4 hours)
2. The expectation and the covariance matrix under linear transformation. (2 hours)
3. Calculations of confidence areas and simultaneous confidence intervals. (4 hours)
4. Hotelling’s T^2 tests. (4 hours)
5. Test I. (2 hours)
6. Calculation of principal components. (4 hours)
7. Calculation of canonical variables. (4 hours)
8. Calculation of Bayesian classification rules. (4 hours)
9. Test II. (2 hours)

Metody kształcenia

Traditional lecture (chalk and blackboard only for the most important formulations, proofs, transformations of formulas), during exercises solving previously given tasks (calculation tasks, carrying out proofs with simplifying assumptions).

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

1. The student's preparation for the exercises is verified by checking the knowledge (concepts, properties, theorems, ...) necessary to solve the next task on the list (lack of preparation for the exercises is taken into account in the final grade for the exercises).
Two colloquiums with tasks of varying difficulty, allowing for the assessment of whether the student has achieved the minimum learning outcomes.
2. Written examination (1st term) with questions referring directly to concepts, statements... as well as questions checking the understanding of the acquired knowledge. Make-up exam in oral form, type of questions as above.

The grade for the course consists of the grade for the exercises (40%) and the grade for the exam (60%). The condition for taking the exam is a positive grade from the exercises. The condition for passing the course is a positive grade in the exercises and exam.

Literatura podstawowa

1. T, W. Anderson, An Introduction to Multivariate Statistical Analysis, New York 1960. 
2. M.S. Srivastava, C.G. Kathri, An introduction to multivariate statistics, North-Holland Pub., Amsterdam 1979.

Literatura uzupełniająca

1. G. Strang, Introduction to Linear Algebra, Sixth Edition 2023, ISBN: 978-17331466-7-8

Uwagi

Zmodyfikowane przez dr Ewa Synówka (ostatnia modyfikacja: 03-02-2024 17:04)