Speaker 

Prof. Frances Kuo, UNSW, Australia

Prof. Dirk Nuyens, KU Leuven, Belgium

Prof. Peter Kritzer, RICAM, Austria

Part 1: Introduction to quasi-Monte Carlo methods

Rm 202, NCTS (Astro-Math Bldg., NTU) November 10 (Thu.) 15:30-18:30

This 3-hour mini-course will provide a contemporary review of QMC methods for approximating high dimensional integrals. We will highlight some recent theoretical developments on "lattice rules" and "higher order digital nets". One key  element  is  the  "fast  component-by-  component construction" which yields QMC methods with a prescribed rate of convergence for sufficiently smooth functions. Another key element is the careful selection of parameters called "weights" to ensure that the worst case errors in  an appropriately  weighted  function  space  are bounded independently of the  dimension.  We  will  demonstrate  how  to  use  the available software packages to construct and generate good QMC sample points for a toy integration problem.

Students will be given a small computational project.

Part 2: Applications of quasi-Monte Carlo methods

Rm 202, NCTS (Astro-Math Bldg., NTU)  November 11 (Wed.)9:00-12:00

In  this  3-hour  seminar  we  will  illustrate  how   to   apply   QMC   methods   to   three   different applications: an option pricing problem from mathematical finance, a maximum likelihood parameter  estimation  problem  from  statistics,  and  a  problem  involving  PDEs with random coefficients which can arise from porous  media  flow  in computational physics  and uncertainty quantification. The precise details of these three applications are not crucial. They are selected to demonstrate that we need quite different strategies when it comes to applying QMC methods in practice. We hope that the audience can bring new potential applications, and we might be able to apply similar strategies or we may need to devise new approaches. Ultimately our aim is to encourage interaction and establish new collaborations.