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Models with Uncertainty

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Course Unit Code470-2406/01
Number of ECTS Credits Allocated4 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First Cycle
Year of Study *Third Year
Semester when the Course Unit is deliveredSummer Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
KRA0220Ing. Jan Kracík, Ph.D.
Summary
Mathematical models of real world systems are often loaded with uncertainty caused by random input parameters, model imprecision, imprecise data, etc. Probability theory is often used for repreenting quantifying the uncertainty in the models.
Learning Outcomes of the Course Unit
Students get acquainted with a probabilistic approach to uncertainty in real world models.
Course Contents
Static models with random inputs
Monte Carlo methods
Linear dynamical models with Gaussian noise
Kalman filter
Bayesian approach to inverse problems
Recommended or Required Reading
Required Reading:
JAYNES, Edwin T., BRETTHORST, G. Larry, ed. Probability theory: the logic of science. Cambridge: Cambridge University Press, 2003. ISBN 0-521-59271-2.

ROBERT, Christian P. a George. CASELLA. Monte Carlo statistical methods. 2nd ed. New York: Springer, c2004. ISBN 0-387-21239-6.
JAYNES, Edwin T., BRETTHORST, G. Larry, ed. Probability theory: the logic of science. Cambridge: Cambridge University Press, 2003. ISBN 0-521-59271-2.

ROBERT, Christian P. a George. CASELLA. Monte Carlo statistical methods. 2nd ed. New York: Springer, c2004. ISBN 0-387-21239-6.

MANDL, Petr. Pravděpodobnostní dynamické modely. Praha: Academia, 1985. Československá akademie věd.
Recommended Reading:
W.H. Press, B.P. Flannery, S.A. Teukolski, W.T. Vetterling, Numerical Recipes in C. Cambridge University Press, 1990.

W. E. Boyce, R. C. DiPrima: Elementary differential equations. Wiley, New York 1992
Vitásek, E.: Numerické metody. SNTL Praha, 1987.

W. E. Boyce, R. C. DiPrima: Elementary differential equations. Wiley, New York 1992
Planned learning activities and teaching methods
Tutorials, Project work
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Graded creditGraded credit100 51