All the contents have been moved to the course Moodle and the new material will be added regularly there.
Examples 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).
September 2th, 2022:
Beginning of lectures: Tuesday, 20.09.2022 at 14:15 at HG F3. Exercises start on 27.09.2022 at 16:15 in HG G 3.
- All materials for the lecture (script, slides, exercises, solutions, and additional notes) will be provided on the Moodle online learning platform: Stochastic Simulation Moodle
- Slides used in the course will be available in due time. Exercises as well as solutions will also be provided.
- More information and the full schedule is available in the organization sheet
Exercises will be held roughly bi-weekly, but on an irregular schedule. The statistical software package R is recommended for solving the exercises. The exercises will take place at the specified date from 16.15-18.00 at HG G 3. The schedule is available in the organization sheet.
Series and solutions
Only phd students who are not taking the exam need to hand-in at least 5 well-solved exercises in order to get credits for the course. All other students do not need to hand in the exercises. You can hand in your solution during the class or by email until the designated date and will receive some feedback in due time. You can find the due date for each exercise in the organization sheet.
- G. S. Fishman, A First Course in Monte Carlo. Thomson Brooks/Cole, 2006.
- S. M. Ross. Simulation. Academic Press, 2012 (5th edition).
Books on a similar level as the course
- Ch. Robert and G. Casella. Introducing Monte Carlo Methods with R. Springer Science & Business Media, 2009.
- Ch. Robert, G. Casella. Monte Carlo Statistical Methods. Springer 2004 (2nd edition).
- S. Asmussen, P. W. Glynn, Stochastic Simulation, Algorithms and Analysis. Springer, 2007.
- P. Glasserman, Monte Carlo Methods in Financial Engineering. Springer 2004.
- B. D. Ripley. Stochastic Simulation. Wiley, 1987.
- W. R. Gilks, S. Richardson, D. J. Spiegelhalter. Markov Chain Monte Carlo in Practice. Chapman & Hall, 1996.
- S. Brooks, A. Gelman, G. Jones, and X.L. Meng, eds. Handbook of Markov Chain Monte Carlo. CRC press, 2011.