M7070 Mathematical Statistics

Přírodovědecká fakulta
podzim 2025

Předmět se v období podzim 2025 nevypisuje.

Rozsah
0/2. 2 kr. Ukončení: z.
Vyučováno kontaktně
Vyučující
Mgr. Andrea Kraus, M.Sc., Ph.D. (přednášející)
doc. Mgr. David Kraus, Ph.D. (přednášející)
Garance
doc. Mgr. David Kraus, Ph.D.
Ústav matematiky a statistiky – Ústavy – Přírodovědecká fakulta
Dodavatelské pracoviště: Ústav matematiky a statistiky – Ústavy – Přírodovědecká fakulta
Předpoklady
Knowledge of calculus and linear algebra at the level of introductory courses of the first two years. Knowledge of probability and statistics at the level of courses M3121 and M4122.
Omezení zápisu do předmětu
Předmět je otevřen studentům libovolného oboru.
Cíle předmětu
The course offers a more detailed view of key concepts of mathematical statistics, e.g., a general concept of random variables, expectations, conditioning, (multivariate) normal distribution, and asymptotics. These concepts facilitate the understanding of the reasons behind validity and properties of the majority of statistical methods. A deep understanding of these concepts enables the students to assess the validity of a given statistical method and modify it, if needed, for multifaceted practice. The course is suitable for students with a deeper interest in mathematical statistics, including those who are planning or beginning doctoral studies in statistics and related fields. It can also serve as a (rather ambitious) way of gaining an overview for students preparing themselves for final exams.
Výstupy z učení
After the course, the students understand general concepts and properties of random variables, expectations, conditioning, (multivariate) normal distribution, asymptotics and the maximum likelihood method. A deep understanding of these concepts enables the students to assess the validity of a given statistical method and modify it, if needed, for multifaceted practice.
Osnova
  • Random variables.
  • Expectation and its properties.
  • Conditional expectation, its properties and computation.
  • Conditional probability and conditional distribution.
  • Multivariate normal distribution.
  • Types of convergence of random variables.
  • Tools for asymptotic statistics.
  • Maximum likelihood, motivation for and use of regularity conditions, asymptotic properties of maximum likelihood estimators, maximum likelihood for confidence regions and hypothesis testing.
Literatura
  • CASELLA, George a Roger L. BERGER. Statistical inference. 2nd ed. Pacific Grove, Calif.: Duxbury, 2002, xxviii, 66. ISBN 8131503941. info
  • PANARETOS, Victor M. Statistics for mathematicians : a rigorous first course. Switzerland: Springer International Publishing, 2016, xv, 177. ISBN 9783319283395. info
  • POLLARD, David. A user's guide to measure theoretic probability. Cambridge: Cambridge University Press, 2002, xiii, 351. ISBN 0521802423. info
  • KALLENBERG, Olav. Foundations of modern probability. 2nd ed. New York: Springer, 2002, xvii, 638. ISBN 0387953132. info
Výukové metody
Interactive lectures combined with exercises, where an active participation of students is expected.
Metody hodnocení
Assignments
Vyučovací jazyk
Angličtina
Informace učitele
The course is taught in a hybrid way (on-site sessions can be accessed online).
Další komentáře
Výuka probíhá každý týden.
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