Stochastic Simulation
Autumn semester 2016
General information
Lecturer  Dr. Fabio Sigrist 

Assistants  Sylvain Robert 
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

August 30th, 2016:
Beginning of lecture: Tuesday, 20/09/2016. (Exercises start on 27/09/2016 at 16:15). 
September 19th, 2016:
Lecture notes and slides for the first lecture are online. 
September 23rd, 2016:
Rcode for the example shown in class and slides for next lecture are online. 
September 29th, 2016:
New versions of slides and lecture notes are now online. 
October 10th, 2016:
Slides for lecture 4, series 2 and solution to series 1 are now online. 
October 14th, 2016:
Slides for lecture 5 online. 
October 19th, 2016:
Series 3 online. 
October 24th, 2016:
Slides for lecture 6 online. 
October 26th, 2016:
Rcode for lecture 5 and series 4 online. 
November 2nd, 2016:
Updated version of slides for lectures 2 and 3, and of the organisation sheet. 
November 28th, 2016:
Series 6 online and new version of the organisation sheet. 
November 29th, 2016:
Slides for lecture 11 online. New version of the script (reversible jump MCMC updated).
Course materials
 Lecture Notes (subject to change during the semester)
 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  20/09  LLL  Introduction, distribution of estimators: trimmed mean, Bootstrap, Simulation in Bayesian statistics 
2  27/09  LLE  Simulation in Statistical Mechanics and Operations Research 
3  04/10  LLL  Simulation in Financial Mathematics, other applications, accuracy of MC methods 
4  11/10  LLE  Generating uniform random variables 
5  18/10  LLL  Quantile transformation, rejection sampling, relations between distributions, permutations 
6  25/10  LLE  Importance sampling , simulation of stochastic differential equations 
7  01/11  LLE  Variance reduction: antithetic variables, control variates, importance sampling 
8  08/11  LLL  Quasi MonteCarlo, introduction MCMC, basics of Markov chains 
9  15/11  LLE  MetropolisHastings Algorithm 
10  22/11  LLL  Independence sampler, random walk Metropolis, componentwise modification, Gibbs sampler 
11  29/11  LLE  Hamiltonian MCMC, MetropolisHastings for variable dimension models 
12  06/12  LLL  MetropolisHastings for variable dimension models (cont.), reversible jump MCMC 
13  13/12  LLL  Accuracy of MCMC approximations 
14  20/12  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
Submitting solutions to the exercise is not compulsory except for some phd students. 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  Topic  Exercises  Solutions  Due date 

27/09  Distribution of estimators  Series 1  04/10  
11/10  Bayes and Ising  Series 2  18/10  
25/10  Generation of random variables  Series 3  01/11  
01/11  Importance sampling  Series 4  08/11  
15/11  Control variates and Antithetic variables  Series 5  22/11  
29/11  MCMC: Gibbs sampler, random walk Metropolis algorithm  Series 6  06/12  
13/12  Hamiltonian MC  Series 7 (schools.csv)  20/12 
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.