Stochastic Simulation
Autumn semester 2018
General information
Lecturer  Dr. Fabio Sigrist 

Assistants  Niklas Pfister 
Lectures  Tue 1417 ML F 36 >> 
Exercises  Tue 1617 (≈ biweekly) ML F 36 >> 
Course catalogue data  >> 
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, acceptreject, 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 (MetropolisHastings, Gibbs sampler, Hamiltonian Monte Carlo, reversible jump MCMC).
Announcements

September 14th, 2018:
Beginning of lecture: Tuesday, 18/09/2018. (Exercises start on 25/09/2018 at 16:15).
Course materials
 Lecture Notes
 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  18/09  LLL  Introduction, distribution of estimators, simulation in Bayesian statistics

2  25/09  LLE  Simulation in statistical mechanics and operations research

3  02/10  LLL  Simulation in financial mathematics, MC integration, accuracy of MC methods

4  09/10  LLE  Generating uniform random variables

5  16/10  LLL  Quantile transformation, rejection sampling, relations between distributions, permutations

6  23/10  LLE  Importance sampling , simulation of stochastic differential equations

7  30/10  LLE  Variance reduction: antithetic variables, control variates, importance sampling

8  06/11  LLL  Quasi MonteCarlo, introduction MCMC, basics of Markov chains

9  13/11  LLE  MetropolisHastings algorithm

10  20/11  LLL  Independence sampler, random walk Metropolis, componentwise modification, Gibbs sampler

11  27/11  LLE  Hamiltonian Monte Carlo, introduction to reversible jump MCMC

12  04/12  LLL  Reversible jump MCMC

13  11/12  LLE  Accuracy of MCMC approximations

14  18/12  LLL  reserve / buffer 
Exercise classes
Exercises will be held roughly biweekly, 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 16.1517.00 in the same place as the lectures.
Series and solutions
Only phd students who are not taking the exam need to handin at least 5 wellsolved 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 

25/09  Series 1  Solution  02/10 
09/10  Series 2  Solution  16/10 
23/10  Series 3  Solution  30/10 
30/10  Series 4  Solution  06/11 
13/11  Series 5  Solution  20/11 
27/11  Series 6  Solution  06/12 
11/12  Series 7  Solution  18/12 
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.