M7986 Statistical inferences I

Faculty of Science
Autumn 2026
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
doc. PaedDr. RNDr. Stanislav Katina, Ph.D. (lecturer)
Mgr. Miriam Kánová (seminar tutor)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 8:00–9:50 M2,01021
  • Timetable of Seminar Groups:
M7986/01: Wed 18:00–19:50 MP1,01014, M. Kánová
M7986/02: Tue 18:00–19:50 MP2,01014a, M. Kánová
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
Abstract
The course covers the foundations of parametric statistical inference. It begins with the path from a scientific question to an inferential claim and defines the position of statistical inference within statistics and data science. The course progressively develops probability and statistical models, likelihood-based reasoning, properties of estimators, simulation experiments, goodness-of-fit assessment, and the general theory of statistical hypotheses. Emphasis is placed on mathematical derivations, the relationships among the Wald, score, and likelihood-ratio principles, Monte Carlo verification of the properties of statistical methods, implementation in R, statistical geometry, and graphical communication. Students learn to connect a scientific question and observed data with a probability model, parameter estimation, uncertainty quantification, hypothesis testing, power, and scientifically appropriate interpretation.
Learning outcomes
  • distinguish descriptive, comparative, predictive, causal, and decision-oriented scientific questions;
  • connect a scientific objective with an effect estimate, study design, model, expression of estimation uncertainty, and corresponding inferential claim;
  • explain the complementary roles of the data scientist, statistician, statistical programmer, data manager, data engineer, and domain expert;
  • formulate an appropriate probability model and statistical model for a given scientific problem;
  • construct, maximise, and interpret a likelihood function and its logarithm;
  • explain and assess the principal finite-sample and asymptotic properties of estimators;
  • compare classical and robust summaries under controlled data contamination;
  • use interpretable and variance-stabilising transformations and the delta method;
  • design, implement, and interpret Monte Carlo experiments for estimators, statistical tests, and confidence intervals;
  • distinguish model-based Monte Carlo simulation, parametric bootstrap, and nonparametric bootstrap;
  • use order statistics, empirical distribution functions, and methods for assessing goodness of fit;
  • formulate statistical hypotheses and define critical regions, p-values, confidence sets, power functions, and the minimum sample size;
  • derive and implement Wald procedures, score procedures, and likelihood-ratio procedures in R;
  • clearly communicate assumptions, calculations, uncertainty, and the results of real-data analyses.
Key topics
  • scientific questions, target populations, effect estimates, study planning, data quality, and inferential claims;
  • the position of statistical inference within statistics and data science and the complementary roles of individual professionals;
  • probability and statistical models, mixture distributions, and nested families of distributions;
  • likelihood, log-likelihood, relative likelihood, score function, parameter, parameter vector, Hessian matrix, Fisher information, and Fisher information matrix;
  • maximum-likelihood estimation and numerical optimisation;
  • statistics, sufficient statistics, sampling distributions, bias, variance, mean squared error, consistency, and efficiency;
  • transformations of distribution parameters and the delta method;
  • pseudorandom-number generation, Monte Carlo simulation, parametric bootstrap, and nonparametric bootstrap;
  • null and alternative hypotheses, critical values, critical regions, p-values, and confidence sets;
  • coverage probability, Type I error, Type II error, and power;
  • the Wald principle, score principle, and likelihood-ratio principle;
  • order statistics, empirical distribution functions, and goodness-of-fit assessment;
  • implementation and statistical graphics in R.
Study resources and literature
    recommended literature
  • CASELLA, George and Roger L. BERGER. Statistical inference. 2nd ed. Pacific Grove, Calif.: Duxbury, 2002, xxviii, 66. ISBN 8131503941. info
  • COX, D. R. Principles of statistical inference. 1st ed. Cambridge: Cambridge University Press, 2006, xv, 219. ISBN 0521685672. info
  • KATINA, Stanislav; Miroslav KRÁLÍK and Adéla HUPKOVÁ. Aplikovaná štatistická inferencia I. Biologická antropológia očami matematickej štatistiky (Applied statistical inference I). 1. vyd. Brno: Masarykova univerzita, 2015, 320 pp. ISBN 978-80-210-7752-2. info
Approaches, practices, and methods used in teaching
Lectures 2 hours per week.
Practicals 2 hours per week. 
Method of verifying learning outcomes and course completion requirements

Method of assessment of learning outcomes: submission of solutions to practical-class exercises, preparation and defence of a project, and an oral examination. Attendance and active participation in practical classes are required to fulfil the in-term requirements and to be admitted to the oral examination; no more than two unexcused absences are permitted. This course-specific allowance is established consistently with Section 9(7) of the Masaryk University Study and Examination Regulations, under which a student is entitled to one unexcused absence from compulsory classes and the course guarantor may permit a higher number where the teaching and study conditions allow it. An absence from compulsory teaching is regarded as excused only if the student submits the excuse through IS MU within five working days after the respective class, in accordance with Section 9(8) of the Masaryk University Study and Examination Regulations. An email or MS Teams message does not replace an excuse submitted through IS MU. The solution to each practical-class exercise must be submitted to the designated submission folder in IS MU no later than Sunday at 23:59 in the week following the week in which the respective practical class took place. The project must be submitted to the designated submission folder in IS MU by the specified deadline. The project defence will take place during the last teaching week of the semester or during the first week after the end of teaching. The resulting assessment of the in-term component, comprising practical-class performance and submissions, the project, and its defence, constitutes 40% of the overall course assessment. This component assessment is not entered separately in IS MU. The oral examination constitutes the remaining 60%. A final course grade can be awarded only if the student has successfully completed every compulsory component. Assessment may be conducted in Czech, Slovak, or English, according to the student’s choice. The conditions may be clarified where required by binding measures adopted by public authorities or Masaryk University. Any such clarification will be announced through IS MU.

Language of instruction
Czech
Follow-Up Courses
Teacher's information

Lectures will be held either in person or online via MS Teams. Practical classes will be held in person only. The form of teaching may change depending on the epidemiological situation and the restrictions in force. Lectures are conducted mainly in Czech or Slovak and, when necessary, in English. The relevant terminology is always also provided with its English equivalents. The intended study skills include the ability to use English both passively and actively within the student’s own field and in potential areas of application of mathematics and statistics. Written records of the lectures in HTML format will be available in IS. The records will be published in advance, topic by topic, always before teaching of the respective topic begins. A single topic may be covered in one or more lectures.

Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024, Autumn 2025.
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