401-3612-00L  Stochastic Simulation

SemesterAutumn Semester 2018
LecturersF. Sigrist
Periodicitytwo-yearly recurring course
Language of instructionEnglish



Courses

NumberTitleHoursLecturers
401-3612-00 GStochastic Simulation3 hrs
Tue14:15-17:00ML F 36 »
F. Sigrist

Catalogue data

AbstractThis course provides an introduction to statistical Monte Carlo methods. This includes applications of simulations in various fields (Bayesian statistics, statistical mechanics, operations research, financial mathematics), algorithms for the generation of random variables (accept-reject, importance sampling), estimating the precision, variance reduction, introduction to Markov chain Monte Carlo.
ObjectiveStochastic simulation (also called Monte Carlo method) is the experimental analysis of a stochastic model by implementing it on a computer. Probabilities and expected values can be approximated by averaging simulated values, and the central limit theorem gives an estimate of the error of this approximation. The course shows examples of the many applications of stochastic simulation and explains different algorithms used for simulation. These algorithms are illustrated with the statistical software R.
ContentExamples of simulations in different fields (computer science, statistics, statistical mechanics, operations research, financial mathematics). Generation of uniform random variables. Generation of random variables with arbitrary distributions (quantile transform, accept-reject, importance sampling), simulation of Gaussian processes and diffusions. The precision of simulations, methods for variance reduction. Introduction to Markov chains and Markov chain Monte Carlo (Metropolis-Hastings, Gibbs sampler, Hamiltonian Monte Carlo, reversible jump MCMC).
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 / NoticeFamiliarity with basic concepts of probability theory (random variables, joint and conditional distributions, laws of large numbers and central limit theorem) will be assumed.

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
Additional information on mode of examinationLanguage of examination: English or German / Prüfungssprache: Deutsch oder Englisch
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

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Only public learning materials are listed.

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Offered in

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