Institute for Mathematical Sciences Event Archive
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Workshop on New Directions in Stein's Method
(18 - 29 May 2015)
Organizing Committee · Visitors and Participants · Overview · Activities · Venue
Chair
- Larry Goldstein (University of Southern California)
- Adrian Röllin (National University of Singapore)
Members
- Andrew Barbour (University of Zürich)
- Louis Chen (National University of Singapore)
- Peter Eichelsbacher (Ruhr-Universität Bochum)
- Giovanni Peccati (University of Luxembourg)
- Nicolas Privault (Nanyang Technological University)
- Gesine Reinert (Oxford University)
One of the greatest accomplishments of probability theory is its success in expressing specific aspects of complicated random phenomena by means of relatively simple limiting distributions. These limits often exhibit a certain “universality” in that they depend only on the most fundamental properties of the models of interest. The classical central limit theorem is the prototype of such results, stating that, under some rather weak moment conditions, a sum of independent random variables, normalised appropriately, will converge to a Gaussian distribution. With approximations of finite systems by their limits, both in theory and applications, comes the need to bound the approximation error, and it is here where Stein's method, introduced in 1970 by Charles Stein, has played an important role over the last few decades.
Perhaps the main advantage of the method is its robustness with respect to dependence in probabilistic models. The method is by no means confined to sums, or to independent random variables, or to approximating distributions such as the normal, which has a nice and explicit probability density function. Indeed, Stein’s method for both normal and non-normal approximations has found applications in a large variety of areas, including statistics, point process theory, combinatorics, number theory, random graph theory, random matrix theory, and statistical physics, to name but a few.
The past two programmes in 2003 and 2008, and a workshop in 2009, all held at IMS, illustrate both the variety and the depth of the field, which has continued to grow since then. The combination of Malliavin calculus and Stein’s method has proved to be very fruitful, having been applied not only to functionals of Gaussian fields, but also to functionals of Rademacher sequences and Poisson point processes. The use of Stein couplings to prove concentration of measure inequalities has opened a new avenue for handling complicated systems exhibiting genuine dependence. Stein’s method has also been extended to obtain very refined moderate deviation results. Multivariate normal approximation, technically notoriously difficult, has seen important developments, for example pushing the dependence on the dimensionality towards the optimal range. Various new distributional transforms have been discovered and successfully combined with Stein’s method.
Considering the diversity and the new exciting directions of recent advances, we believe now is the right time to organise a comprehensive workshop on Stein's method and its applications. We plan to bring together not only active researchers directly working in the area, but also those who apply Stein's method in their work in order to stimulate, strengthen and develop existing interactions between theory and practice. The National University of Singapore has long been a centre of research in Stein's method, having been the base of major programmes and the home to a number of researchers who have been influential in its development. The combination of these many factors makes Singapore a natural place in which to conduct the workshop, with the resulting benefit of fostering collaborations, both locally and internationally.
08:40am - 08:50am |
Registration |
08:50am - 09:00am |
Opening Remarks |
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Chair: Larry Goldstein, University of Southern California |
09:00am - 09:45am |
Cramer type moderate deviations by Stein's method (PDF) |
09:45am - 10:30am |
Error bounds for the random sums CLT by Stein's method of normal approximation |
10:30am - 11:00am |
--- Group Photo & Coffee Break --- |
11:00am - 11:45am |
Monotone couplings: Stein's method and beyond (PDF) |
11.45am - 01:15pm |
--- Lunch --- |
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Chair: Nathan Ross, The University of Melbourne, Australia |
01:15pm - 02:00pm |
Stein's method for alpha-stable distributions |
02:00pm - 02:30pm |
--- Coffee Break --- |
02:30pm - 03:15pm |
Central limit theorems and bootstrap in high dimensions (PDF) |
Tuesday, 19 May 2015 |
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08:50am - 09:00am |
Registration |
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Chair: Giovanni Peccati, University of Luxembourg, Luxembourg |
09:00am - 09:45am |
Stein's method and functionals of convex hulls (PDF) |
09:45am - 10:30am |
Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to U-statistics and stochastic geometry |
10:30am - 11:00am |
--- Coffee Break --- |
11:00am - 11:45am |
Kolmogorov Berry-Esseen bounds for binomial functionals (PDF) |
11.45am - 01:15pm |
--- Lunch --- |
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Chair: Jay Bartroff, University of Southern California, USA |
01:15pm - 02:00pm |
Isolated points in the random connection model |
02:00pm - 02:30pm |
--- Coffee Break --- |
02:30pm - 03:15pm |
Steining the steiner formula (PDF) |
06:15pm |
Dinner (Volunteer and self paid) |
Wednesday, 20 May 2015 |
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08:50am - 09:00am |
Registration |
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Chair: Dominic Schuhmacher, Georg-August-Universität Göttingen, Germany |
09:00am - 09:45am |
Distributional limits for (i) a new family of Polya urn models with immigration or (ii) preferential attachment networks where entering nodes having a random number of initial edges |
09:45am - 10:30am |
Stein approximation for Ito and Skorohod integrals by Edgeworth type expansions |
10:30am - 11:00am |
--- Coffee Break --- |
11:00am - 11:45am |
Malliavin-Stein method for Variance-Gamma approximation on Wiener space (PDF) |
11.45am - 01:15pm |
--- Lunch Reception at IMS --- |
02:00pm |
Excursion: Gardens by the Bay (Volunteer and self paid) |
Thursday, 21 May 2015 |
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08:50am - 09:00am |
Registration |
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Chair: Ivan Nourdin, Université du Luxembourg, Luxembourg |
09:00am - 09:45am |
On the use of Markov triplets for limit theorems and moment inequalities (PDF) |
09:45am - 10:30am |
A second order Poincar\'e inequality for functionals of general Poisson processes (PDF) |
10:30am - 11:00am |
--- Coffee Break --- |
11:00am - 11:45am |
Limit theorems for Poisson U-statistics (PDF) |
11.45am - 01:15pm |
--- Lunch --- |
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Chair: Gesine Reinert, University of Oxford, UK |
01:15pm - 02:00pm |
Beating log-Sobolev, one Stein's kernel at a time (PDF) |
02:00pm - 02:30pm |
--- Coffee Break --- |
02:30pm - 04:05pm |
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02:30pm - 02:55pm |
Short Talks: On bounds in multivariate Poisson approximations (PDF) |
02:55pm - 03:20pm |
Short Talks: Approximating the CLT using Stein's method (PDF) |
03:20pm - 03:45pm |
Short Talks: Conditional distribution approximation with birth death processes (PDF) |
03:45pm - 04:05pm |
Short Talks: Concentration inequalities by Stein couplings (PDF) |
Friday, 22 May 2015 |
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08:50am - 09:00am |
Registration |
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Chair: Erol Peköz, Boston University, USA |
09:00am - 09:45am |
Bounds to the normal for group sequential statistics with covariates (PDF) |
09:45am - 10:30am |
Mixing times for abelian sandpiles |
10:30am - 11:00am |
--- Coffee Break --- |
11:00am - 11:45am |
A canonical approach to Stein's density approach (PDF) |
11.45am - 01:15pm |
--- Lunch --- |
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Chair: Mathew Penrose, University of Bath, UK |
01:15pm - 02:00pm |
Stein's method and the many-worlds interpretation of quantum mechanics (PDF) |
02:00pm - 02:30pm |
--- Coffee Break --- |
02:30pm - 03:15pm |
Matrix concentration inequalities via the method of exchangeable pairs |
08:40am - 08:50am |
Registration |
08:50am - 09:00am |
Opening Remarks |
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Chair: Adrian Roellin, National University of Singapore |
09:00am - 09:45am |
Progress using Stein's method for strong embeddings (PDF) |
09:45am - 10:30am |
Stein's method for Gibbs point process approximation (PDF) |
10:30am - 11:00am |
--- Coffee Break --- |
11:00am - 11:45am |
Stein's method for steady-state diffusion approximations (PDF) |
11.45am - 01:15pm |
--- Lunch --- |
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Chair: Neelesh Upadhye, Indian Institute of Technology Madras, India |
01:15pm - 02:00pm |
On the probability approximation of spatial point processes (PDF) |
02:00pm - 02:30pm |
--- Coffee Break --- |
02:30pm - 03:15pm |
Multivariate normal approximation: permutation statistics, local dependence and beyond (PDF) |
Tuesday, 26 May 2015 |
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08:50am - 09:00am |
Registration |
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Chair: Peter Eichelsbacher, Ruhr-University of Bochum, Germany |
09:00am - 09:45am |
Some applications of Stein's method to number theory (PDF) |
09:45am - 10:30am |
Stein's method and subsequence problems (PDF) |
10:30am - 11:00am |
--- Coffee Break --- |
11:00am - 11:45am |
On the weak convergence of Poisson-Mixture sums via Stein's method (PDF) |
11.45am - 01:15pm |
--- Lunch --- |
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Chair: Yvik Swan, Université de Liège, Belgium |
01:15pm - 02:00pm |
Gaussian and bootstrap approximations to suprema of empirical processes (PDF) |
02:00pm - 02:30pm |
--- Coffee Break --- |
02:30pm - 03:15pm |
Coupling the binary tree with continuum random tree and more |
Wednesday, 27 May 2015 |
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08:50am - 09:00am |
Registration |
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Chair: Aihua Xia, The University of Melbourne, Australia |
09:00am - 09:45am |
Stein couplings for normal approximation |
09:45am - 10:30am |
General normal approximation with applications to random measures and Stein couplings (PDF) |
10:30am - 11:00am |
--- Coffee Break --- |
11:00am - 11:45am |
Stein's method and characteristic functions (PDF) |
Thursday, 28 May 2015 |
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08:50am - 09:00am |
Registration |
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Chair: Nicolas Privault, Nanyang Technological University |
09:00am - 09:45am |
Random graphs, the Chen-Stein method and networking applications (PDF) |
09:45am - 10:30am |
The Stein-Dirichlet-Malliavin method and applications to stochastic geometry (PDF) |
10:30am - 11:00am |
--- Coffee Break --- |
11:00am - 11:45am |
Bounds with data and an almost sure central limit theorem using Stein's method (PDF) |
11.45am - 01:15pm |
--- Lunch --- |
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Chair: Andrew Barbour, The University of Melbourne, Australia |
01:15pm - 02:00pm |
Poisson approximation for two scan statistics with rates of convergence (PDF) |
02:00pm - 02:30pm |
--- Coffee Break --- |
02:30pm - 04:05pm |
Short Talks |
02:30pm - 02:55pm |
Short Talks: On Stein operators for discrete approximations (PDF) |
02:55pm - 03:20pm |
Short Talks:Stein's method for steady-state diffusion approximation of waiting times in a G/G/1 queue |
Friday, 29 May 2015 |
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08:50am - 09:00am |
Registration |
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Chair: Louis Chen, National University of Singapore |
09:00am - 09:45am |
Rates of convergence for multivariate normal approximations by Stein's method (PDF) |
09:45am - 10:30am |
Multivariate approximation in total variation I (PDF) |
10:30am - 11:00am |
--- Coffee Break --- |
11:00am - 11:45am |
Multivariate approximation in total variation II (PDF) |
Students and researchers who are interested in attending these activities are requested to complete the online registration form.
The following do not need to register:
- Those invited to participate.
Organizing Committee · Visitors and Participants · Overview · Activities · Venue
