Stochastic Simulation

Autumn semester 2020

General information

The lectures and exercise classes will take place online.

Lecturer Dr. Fabio Sigrist
Assistants Yulia Kulagina
Lectures Tue 14:15-17:00
Exercises Tue 16:15-17:00 (≈ biweekly)
Course catalogue data >>


All the contents have been moved to the course Moodle and the new material will be added regularly there.

Course content

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).

Course materials

  • 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

Week Date Lecture/Exercise Topic
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
9 10/11 L-L-E Metropolis-Hastings algorithm
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

Exercise classes

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.

Date Exercises Solutions Due date
22/09 Series 1 Solution 29/09
06/10 Series 2 Solution 13/10
20/10 Series 3 Solution 27/10
27/10 Series 4 Solution 03/11
10/11 Series 5 Solution 17/11
24/11 Series 6 Solution 01/12
08/12 Series 7 Solution 15/12

Introductory books

  • 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.