#
MU:MU11185 Applied Statistics II - Course Information

## MU11185 Applied Statistics II

**Mathematical Institute in Opava**

Summer 2023

**Extent and Intensity**- 2/1/0. 3 credit(s). Type of Completion: zk (examination).
**Teacher(s)**- RNDr. Jaroslav Bradík (lecturer)
**Guaranteed by**- RNDr. Oldřich Stolín, Ph.D.

Mathematical Institute in Opava **Prerequisites**- (
**MU20027**Applied Statistics I ||**MU11160**Applied Statistics ) && TYP_STUDIA ( B )

The student is supposed to be acquainted with the material covered in Applied statistics. **Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.
**fields of study / plans the course is directly associated with**- Data Analysis (programme MU, Bc-M)
- Mathematical Methods and Modelling (programme MU, Bc-M)
- Mathematical Methods in Economics (programme MU, Bc-M)
- Mathematical Methods in Risk Management (programme MU, Bc-M)
- General Mathematics (programme MU, Bc-M)

**Course objectives**- The course Applied Statistics consists of lectures and tutorials whose goal is to introduce students to Bayesian statistics and its practical methods.
**Syllabus**- 1. Statistical models.

2. The geometry of the space of probability distributions.

3. Singular statistical models.

4. Variational Bayesian methods.

5. Hierarchical models

6. Pseudo-Bayesian methods: Expectation-maximization algorithm. Empirical Bayesian methods.

7. First encounter with stochastic differential equations.

8. Kalman filters.

9. Dynamic filters.

10. Purposeful control under random influences.

- 1. Statistical models.
**Literature**- Christian P. Robert.
*The Bayesian choice: From decision-theoretic foundations to computational implementation*. New York, 2007. info

*required literature*- Sumio Watanabe.
*Algebraic geometry and statistical learning theory*. New York, 2009. ISBN 9780521864671. info - Amari, Shun-ichi and Nagaoka, Hiroshi.
*Methods of Information Geometry*. Oxford University Press, AMS, 2007. info - Christian P. Robert and George Casella.
*Monte Carlo statistical methods*. New York, 2004. info

*recommended literature*- Karl Friston and Klaas Stephan and Baojuan Li and Jean Daunizeau.
*Generalised Filtering, Mathematical Problems in Engineering, Article ID 621670*. 2010. info

*not specified*- Christian P. Robert.
**Language of instruction**- Czech
**Further comments (probably available only in Czech)**- The course can also be completed outside the examination period.
**Teacher's information**- Requirements to pass the course:

Satisfactory completion of all assigned exercises with at most two exceptions.Activity Difficulty [h] Cvičení 10 Domácí příprava na výuku 24 Přednáška 20 Příprava na zápočet 8 Příprava na zkoušku 16 **Summary**78

- Enrolment Statistics (Summer 2023, recent)
- Permalink: https://is.slu.cz/course/sumu/summer2023/MU11185