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 4th, 2020:
Beginning of lectures: Tuesday, 15.09.2020 at 14:15. Exercises start on 22.09.2020 at 16:15.
September 13th, 2020:
All lectures will be recorded. Further, we work with the Moodle online learning platform. The link for this course is: Stochastic Simulation Moodle All materials for the lecture (script, slides, exercises, solutions, lecture recordings and additional notes) will be provided there.
September 14th, 2020:
Exercise series 1 has been uploaded to Moodle (tab Exercises).
October 6th, 2020:
Exercise series 2 has been uploaded to Moodle (tab Exercises).
- All materials for the lecture (script, slides, exercises, solutions, lecture recordings 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 available in Organization sheet
|1||15/09||L-L-L||Introduction, simulation for determining distributions of estimators, simulation in Bayesian statistics
|2||22/09||L-L-E||Simulation in statistical mechanics and operations research
|3||29/09||L-L-L||Simulation in financial mathematics, MC integration, accuracy of MC methods
|4||06/10||L-L-E||Generating uniform random variables
|5||13/10||L-L-L||Quantile transformation, rejection sampling, relations between distributions, simulation of multivariate normal variables
|6||20/10||L-L-E||Importance sampling, simulation of stochastic differential equations
|7||27/10||L-L-E||Variance reduction: antithetic variables, control variates, importance sampling
|8||03/11||L-L-L||Quasi Monte-Carlo, introduction MCMC, basics of Markov chains
|10||17/11||L-L-L||Independence sampler, random walk Metropolis, componentwise modification, Gibbs sampler
|11||24/11||L-L-E||Hamiltonian Monte Carlo, introduction to reversible jump MCMC
|12||01/12||L-L-L||Reversible jump MCMC
|13||08/12||L-L-E||Accuracy of MCMC approximations
|14||15/12||L-L-L||reserve / buffer|
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 16.15-17.00 in the same way as the lectures.
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.
- 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.