Basic information
RNDr. Radim Navrátil, Ph.D.
Basic information
RNDr. Radim Navrátil, Ph.D.
Basic information
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jaro 2023

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Examination in progress.  Last date: Tuesday 27th of June at 12:30.


Course outline

  • Introduction to statistics. Data preprocessing
  • Exploratory data analysis (descriptive statistics, data visualization)
  • Brief review of probability theory
  • Probability distributions. Central limit theorem
  • Point estimates (maximum likelihood method, method of moments)
  • Confidence intervals, testing of statistical hypotheses
  • Model selection. Normality testing
  • Testing of statistical hypotheses II (two sample tests)
  • ANOVA, tests of independence, contingency tables
  • Nonparametric tests
  • Linear regression model (revision and generalization)
  • Modern methods - Monte Carlo simulations, bootstrap
  • Revision


Prerequisities

  • Basic knowledge of mathematical analysis: functions, limits of sequences and functions, derivations and integral for real and multidimensional  functions.
  • Basic knowledge of linear algebra: matrices and determinants, eigenvalues and eigenvectors.
  • Basic knowledge of probability theory: probability, random variables and vectors, limit theorems.
  • Basic knowledge of linear regression models.


Review (self study) of probability theory

  • Sigma algebra, probability measure and its properties, Kolmogorov definition of probability, conditional probability, independent events.
  • Random variables and vectors, their distributions, properties and connections. Discrete and continuous random variables and random vectors, their distributions. Numerical characteristics of random variables and random vectors. Independent random variables.
  • Law of large numbers, central limit theorem.
  • Chyba: Odkazovaný objekt neexistuje nebo nemáte právo jej číst.
    https://is.muni.cz/el/fi/jaro2023/MV013/um/literature/All_of_Statistics__A_Concise_Course_in_Statistical_Inference__Springer_Texts_in_Statistics____PDFDrive__.pdf
    Chyba: Odkazovaný objekt neexistuje nebo nemáte právo jej číst.
    https://is.muni.cz/el/fi/jaro2023/MV013/um/literature/casella_berger_statistical_inference1.pdf
  • If students do not have sufficient knowledge the above terms, they have to self-study it.
  • To understand the content of the course, it is essential to master probability theory.
  • Week 3 - 4 : A brief overview of the above terms.
  • From that on, we will assume that all the students know it, even with all details not mentioned in the lectures.


    • Assessment methods

    • 3 homework assignments (you can get together up to 40 points).
    • Final written exam - open notes (you can get up to 60 points).

    Type of Completion:

    • Fulfilling requirements  (Zápočet, Z) - need to get at least 50 points in total.
    • Examination (Zkouška, Zk) - grading:

    100-90A
    89-80B
    79-70C
    69-60D
    59-50E
    49-0F


    The final exam

    • The exam type: written with open notes.
    • Time for the exam: 100 minutes.
    • During the exam, you will be asked to prove your identity (showing your ID).
    • If anybody has recorded disability in Information System and needs special treatment, let me know before the exam (in advance). Subsequent demands will not be taken into account.
    • The exam language is English.
    • The exam will be written. You will write down your solution on separate sheets of paper.
    • You may use any materials available, but communication with others is prohibited.
    • You may use R for computations, but all the relevant results state in your solution (you will not submit your R-code).
    • Google or Wikipedia solutions will not be accepted.
    • The use of ChatBots is strictly forbidden.
    • In case of suspicious solutions and results, you might be subject to an additional oral
      exam.
    • Unreadable solutions will be ignored.
    • Sample exam: 
      Chyba: Odkazovaný objekt neexistuje nebo nemáte právo jej číst.
      https://is.muni.cz/el/fi/jaro2023/MV013/um/MV013-sample-exam2023.pdf

    Seminars

    • The first week (February 14 - 15) optional exercise classes will take place to get familiar with statistical software R and RStudio.
    • Regural exercise classes (seminars) start the second week.
    • Attendance at the seminars is obligatory (two unexcused absences will be tolerated).
    • Only proper excuses will be accepted uploaded into Information System on time).
    • All the students must be assigned to a seminar group (otherwise, you get an "X").
    • There are 2 groups for students who cannot bring their own laptops and 4 groups for students with their own laptops.


    Homework assignments

    • The assignment will be published centrally on Wednesday afternoon/evening (3 times a semester, not regularly). 
    • Deadline: the next Wednesday 23:59 (midnight).
    • Solution (pdf and source code) upload to "Homework vaults" in the Information system.

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