Event
【GIR Open Seminar】Dr. Nicki Holighaus / Austrian Academy of Sciences（Austria）
| Date | 2025.2.10 (13：00 - 14：30) |
|---|---|
| Venue |
Room 204, 2F., Building 3, Koganei Campus, TUAT Meeting ID:836 4540 7210 Passcode:602184 |
| Google Classroom Code | fmk5ljl |
| Speaker | Dr. Nicki Holighaus |
| Affiliation | Austrian Academy of Sciences (Austria) |
| Title | "Fundamentals of Quasi-Monte Carlo Integration" ＜Abstract＞ The Monte Carlo (MC) method is a simple quadrature rule for the approximation of integrals over finite domain or, more generally, probability spaces. Specifically, MC simply approximates an integral by the mean of finitely many samples, taken uniformly at random in the domain of integration. MC is very simple, but only achieves an approximation rate of O(N-1/2), in expectation. Quasi-Monte Carlo (QMC) likewise approximates integrals by the mean of point evaluations, eschewing random points in favor of point sets that are, in an appropriate sense, well-distributed. The Koksma-Hlawka inequality provides a worst-case bound of the integration error in QMC in the form D(P)S(f), where D(P) is a measure of equidistribution of the samples P, usually referred to as discrepancy and S(f) is a measure of smoothness of the integrand f. Crucially, there are sets P that achieve discrepancy of order O(log(N)d/N), significantly improving convergence speed over MC. In this talk, we cover fundamental concepts of QMC, such as Koksma-Hlawka-type error bounds and appropriate measures of discrepancy and smoothness. On the d-dimensional unit square, we will illustrate some constructions of point sets and sequences with low discrepancy. To illustrate that measuring equidistribution of a finite set of points in a domain is somewhat subjective and not necessarily straightforward, I prepared a short survey in which you can test your own intuition on the subject, leading up to the presentation: https://forms.gle/TgfGeexRevajNJMM8 (less than 5 minutes). I will shortly discuss the survey results at the beginning and end of the talk. |
| Language | English |
| Intended for | Everyone is welcome to join. |
| Co-Organized by | Institute of Global Innovation Research "LIFE SCIENCE" Yatabe Team Excellent Leader Development for Super Smart Society by New Industry Creation and Diversity |
| Contact | Institute of Global Innovation Research, Institute of Engineering Associate Prof. Kohei Yatabe e-mail: yatabe（at）go.tuat.ac.jp |
| Remarks | This seminar will be held both face-to-face and online concurrently. |
このページの上部へ