Monte Carlo methods in Scientific computing
- Generating random numbers. The inverse method. Rejection sampling.
- Sequential methods. Sequential importance sampling. Applications.
- Markov chain Monte Carlo methods. The Metropolis-Hastings algorithms and its variants. The Metropolis algorithm. Gibbs sampling.
Generalized Gibbs sampling. Example applications.
- Parallel Markov chains and tempering. Simulated tempering. Parallel tempering. Simulated Annealing.
- Mixing of Markov chains. Relaxation time and the second largest eigenvalue modulus. Conductance, Cheeger inequalities.
- Methods for inferring the speed of convergence. Combinatorial
methods: multicommodity flows. Geometric methods, isoperimetric inequalities. Probabilistic methods: coupling, path coupling, coupling from the past.
By the end of the course, students are enabled to do independent study and research in fields touching on the topics of the course, and how to use these methods to solve specific problems. In addition, they develop some special expertise in the topics covered, which they can use efficiently in other mathematical fields, and in applications, as well. They also learn how the topic of the course is interconnected to various other fields in mathematics, and in science, in gener
Elective live courses: regular homework, and presentation or final