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Selected Topics in Probability and Statistics

Type of study Follow-up Master
Language of instruction English
Code 470-4406/02
Abbreviation VPPS
Course title Selected Topics in Probability and Statistics
Credits 4
Coordinating department Department of Applied Mathematics
Course coordinator Ing. Jan Kracík, Ph.D.

Subject syllabus

Random vector, random field, conditional probability, independence, conditional
independence

Bayes theorem, introduction to Bayesian theory, prior and posterior probability
distribution

Generating random numbers, elementary Monte Carlo methods, Monte Carlo
simulations

Application of Monte Carlo methods in Bayesian statistics

Regression analysis (simple linear regression, multivariate linear regression,
generalized linear models), model selection criteria, Bayesian approach to
regression analysis

Stochastic process (basic definitions and notions), numerical characteristics,
examples of stochastic processes

Introduction to time series analysis

Literature

Kruschke, John. Doing Bayesian data analysis: A tutorial introduction with R. Academic Press, 2010. ISBN 978-0123814852
Cox, David Roxbee, David Victor Hinkley. Theoretical statistics. CRC Press, 1979. ISBN 978-0412161605 
Chatfield, Chris. The analysis of time series: an introduction. CRC press, 2013. ISBN 978-1584883173 

Advised literature

Schervish, Mark J. Theory of statistics. Springer, 1995. ISBN 978-1461242505 
Crawley, Michael J. The R book. John Wiley & Sons, 2012. ISBN 978-0470973929


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