doctoral combined specialized

Included in the programme: PřF D-MA_ Mathematics and Statistics

### Final state doctoral examination and defence of the doctoral thesis

Before submitting an application for a state doctoral exam, the doctoral candidate must have fulfilled all the obligations set out in the individual study plan to this milestone.

Requirement is knowledge of probability theory, mathematical statistics, mathematical and statistical modeling, numerical mathematics and related fields according to the field of the dissertation. The extent of the state doctoral examination is determined by the subjects completed and the focus of the doctoral thesis and three subjects will be chosen to cover the studied scientific discipline and specialization and these subjects will be focused on the exam. Student will choose the areas and sub-areas after consulting the supervisor. Student will consult the specific content of the sub-areas and the literature with the examiner. The areas are selected from the following list:

- Parametric statistical inference,

- Nonparametric statistical inference and smoothing,

- Regression models,

- Computational statistics and multivariate statistical analysis, - Probability theory,

- Numerical modeling,

- Mathematical modeling,

- Dynamic systems.

The doctoral thesis must contain original and published results or results accepted for publication. They may be of a theoretical nature, representing an original implementation into mathematical or statistical software or applications.

### Requirements of the study

The student has at least four semester courses during the course of study outside the content of the doctoral thesis. Upon agreement with the supervisor, an individual study will focus on broadening the knowledge of the given field and on the special parts required for writing the doctoral thesis.

He regularly attends specialized seminars on applied mathematics, statistics, or related disciplines. Helps provide teaching for undergraduate studies.

Research activities:

- Dissertation preparation - takes place during the whole study period and constitutes 60-70% of the workload

- Publications - Papers can be theoretical-methodical and / or bring innovative applications of statistical or mathematical methods in a selected area within the subject of the doctoral thesis (thus proving the knowledge of academic writing).

- Pedagogical activities (participation in teaching) - Ph.D. student can take part in supervising bachelor's theses, chairing seminars, etc., up to a maximum of 150 hours per study (5-10% of the workload)

- The student must present some results of his scientific work on at least two international conferences in the Czech Republic or abroad in English (thus proving the knowledge of professional English). The expected extent of this activity is about 5-15% of the total workload

- Active participation in the seminar of this specialization (5-10% of the workload)

At the latest in the fourth semester, the project of the doctoral thesis must be presented at a seminar organized by the Institute of Mathematics and Statistics MU (e.g. Applied Mathematics Seminar).

Part of the study responsibilities in the doctoral study program is the completion of a part of the study at a foreign institution lasting at least one month or another form of direct student participation in international cooperation.

The basic form of doctoral study is a full-time form. It is expected that if the student will properly fulfill all his / her duties, he / she will successfully complete his / her studies after four years of standard study period (he / she will present the application for defense and defend in the following period). The combined form should be used exceptionally, especially in cases where, for serious reasons, the student fails to finish his studies after 4 years, although he has fulfilled his ISP duties properly. The only task within the combined form is the work on the dissertation project.

### Proposal of dissertation topics and topics of defended dissertations

5 defended disertations:

Stochastic models and statistical analysis of series of events

Mgr. Marie Leváková, školitel Petr Lánský

https://is.muni.cz/auth/th/odd3g/?fakulta=1431

Stochastic methods in analysis of economic data

Mgr. Lenka Křivánková, školitel Martin Kolář

https://is.muni.cz/auth/th/mti78/?fakulta=1431

Statistical inference for stochastic point processes with application on neuronal data

Mgr. Bc. Kamil Rajdl, školitel Petr Lánský

https://is.muni.cz/auth/th/vjs14/?fakulta=1431

Stochastic models with continuous time and their applications (contribution to degradation theory)

prof. Ing. David Vališ, školitel Petr Lánský

https://is.muni.cz/auth/th/e2jbv/?fakulta=1431

Meta-analysis of Clinical Trials

Mgr. Pavla Krajíčková, školitel Gejza Wimmer

https://is.muni.cz/auth/th/crglh/?fakulta=1431