This is the course page of MATS442 Stochastic simulation, lectured in first teaching block of spring 2020 (from 8th January to 21st February 2020). Course page in Sisu

News

• Added details about requirements (regarding the final exam).
• Update to the last problem sheet: there is an extra problem (problem 6 of sheet 5, with additional hint).
• Full set of 2020 lecture notes are available. Thank you for attending the lectures!
• Solutions to problems will appear in Koppa.
• Lecture videos are now available.

Lectures & topics covered

The whole set of lecture notes.

• Lecture 1 (8.1.): Practicalities, the Monte Carlo method, consistency, confidence interval, inverse distribution function method.
• Lecture 2 (9.1.): Discrete random variables, general inverse cdf, Box-Muller transform, other transformations, rejection sampling.
• Lecture 3 (15.1.): Rejection sampling with unnormalised distributions, importance sampling.
• Lecture 4 (16.1.): Rare events, self-normalised importance sampling.
• Lecture 5 (22.1.): Rao-Blackwellisation, stratification, antithetic variables.
• Lecture 6 (23.1.): Control variates, Markov chains, reversibility, Metropolis-Hastings.
• Lecture 7 (29.1.): Independence sampler, Metropolis-Hastings in R^d, random-walk Metropolis
• Lecture 8 (30.1.): Metropolis-within-Gibbs, Gibbs sampling.
• Lecture 9 (5.2.): Convergence of Gibbs, Langevin, Hamiltonian Monte Carlo, burn-in, asymptotic variance.
• Lecture 10 (6.2.): Peskun-Tierney order, state-space model, sequential importance sampling.
• Lecture 11 (12.2.): Particle filter, unbiasedness of PF.
• Lecture 12 (13.2.): Particle MCMC.

Recorded lectures are available in Moniviestin; please check the path key from Koppa.

Problems classes

Fri 8:30–10:00 at MaD355 by Santeri Karppinen.

• Problem sheet 1 (17.1.),
• Problem sheet 2 (24.1.)
• Problem sheet 3 (31.1.) discrete_from_uniform.jl
• Problem sheet 4 (7.2.)
• Problem sheet 5 (14.2.) asymptotic_variance.jl
• Problem sheet 6 (21.2.)

Solutions will appear in Koppa

There are both theoretical questions and computer programming assignments (marked with C) in the problem sheets. In order to collect the points from the problems, (see Requirements below)

• You must be prepared to explain your solutions to theoretical questions to the other students on the blackboard in the problems class
• You must return the programming assignments by email to <santeri.j.karppinen(•at•)jyu.fi> before the class.

In case you cannot attend a problems class, you can return your solutions to the theoretical questions also by email (only PDF files accepted; if scanned hand-written, please write clearly!).

Requirements

In order to pass the course, you need to:

1. Complete at least 15% of the exercise problems.
2. Pass the course exam or the final exam (without the bonus points taken into account).

Completing more than 15% of exercise problems accumulate bonus points as follows:

Completed	15%	30%	45%	60%	75%	90%
Bonus points	—	+1	+2	+3	+4	+5

The grade will be determined from exam points (max. 30) + bonus points. The maximum number of bonus points will increase the final mark by one (at least).

If you have not completed at least 15% of the exercise problems, you can still attend the final exam.

The exams are scheduled Wed 26.2., 11.3. (course exams) and 22.4. (final exam) Please register to the exam in Korppi.

Supporting material

• Monte Carlo statistical methods book by Christian Robert and George Casella. (The 1st ed. is suitable as well)
• Monte Carlo theory, methods and examples, book in progress by Art Owen.
• If you wish to use Julia:
  • The Julia Programming Language; see also the documentation
  • Juno: Julia integrated development ernvironment (IDE) in the Atom editor (similar to RStudio for R); see the installation instructions
• If you wish to use R:
  • An Introduction to R
  • RStudio, open source IDE for R

Contact

If you have any questions, please contact <matti.s.vihola(•)jyu.fi>.