401-3612-00L  Stochastic Simulation

SemesterAutumn Semester 2020
LecturersF. Sigrist
Periodicitytwo-yearly recurring course
Language of instructionEnglish


401-3612-00 GStochastic Simulation
The lecturers will communicate the exact lesson times of ONLINE courses.
3 hrs
Tue14:00-17:00ON LI NE »
F. Sigrist

Catalogue data

AbstractThis course introduces statistical Monte Carlo methods. This includes applications of stochastic simulation in various fields (statistics, statistical mechanics, operations research, financial mathematics), generating uniform and arbitrary random variables (incl. rejection and importance sampling), the accuracy of methods, variance reduction, quasi-Monte Carlo, and Markov chain Monte Carlo.
ObjectiveStudents know the stochastic simulation methods introduced in this course. Students understand and can explain these methods, show how they are related to each other, know their weaknesses and strengths, apply them in practice, and proof key results.
ContentExamples of simulations in different fields (statistics, statistical mechanics, operations research, financial mathematics). Generation of uniform random variables. Generation of random variables with arbitrary distributions (including rejection sampling and importance sampling), simulation of multivariate normal variables and stochastic differential equations. The accuracy of Monte Carlo methods. Methods for variance reduction and quasi-Monte Carlo. Introduction to Markov chains and Markov chain Monte Carlo (Metropolis-Hastings, Gibbs sampler, Hamiltonian Monte Carlo, reversible jump MCMC). Algorithms introduced in the course are illustrated with the statistical software R.
Lecture notesA script will be available in English.
LiteratureP. Glasserman, Monte Carlo Methods in Financial Engineering.
Springer 2004.

B. D. Ripley. Stochastic Simulation. Wiley, 1987.

Ch. Robert, G. Casella. Monte Carlo Statistical Methods.
Springer 2004 (2nd edition).
Prerequisites / NoticeIt is assumed that students have had an introduction to probability theory and statistics (random variables, joint and conditional distributions, law of large numbers, central limit theorem, basics of measure theory).

The course resources (including script, slides, exercises) will be provided via the Moodle online learning platform.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits5 credits
ExaminersF. Sigrist
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationoral 20 minutes
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

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Offered in

DAS in Data ScienceStatisticsWInformation
Data Science MasterCore ElectivesWInformation
Mathematics MasterSelection: Probability Theory, StatisticsWInformation
Statistics MasterStatistical and Mathematical CoursesWInformation
Statistics MasterSubject Specific ElectivesWInformation