18th Meeting of AiOs in Stochastics

17 - 19  MAY  2010

The eighteenth meeting of the AiOs (PhD students) in Stochastics in the Netherlands will take place from 17 - 19  May 2010. This meeting is organized by the AiO Network Stochastics and is supported by the research schools MRI and Stieltjes Institute, and by the mathematics cluster NDNS+. The meetings continue the tradition of AiO meetings following the Bijeenkomst Stochastici in Lunteren, at a different location, a different time,  and in a different format.

The meeting consists of two short courses, one in probability and one in statistics, and lectures by the participants. The purpose is both to learn topics of current research interest and to become acquainted with the work of other aios in the Netherlands.

The short courses are given by Alois Kneip and Ronald Meester. See below for titles and abstracts.
The meeting will start on Monday at 10.30 and will end on Wednesday after lunch. For a detailed programme see below.

The meeting will be held in  building "Stalheim" (see picture)  of
 Conferentie Centrum De Hoorneboeg
 Hoorneboeg 5
 1213 RE Hilversum
  035 - 577 1231

Registration is possible electronically through the registration form.

Conference Fee
The total fee for the conference and two nights overnight stay in building Stalheim and meals from Monday lunch to Wednesday lunch is 224 euros. See the registration form for specifics on payment.

Further Information
For further information contact the organizers Ronald Meester and Geurt Jongbloed, or Maryke Titawano for practical matters.

Detailed Program

Monday Tuesday Wednesday
8-9 breakfast breakfast
9-10 Alois Kneip Zhe Guo / Henk Don
10.00-10.30 coffee coffee
10.30-11.30 arrival/coffee Ronald Meester Ronald Meester
11.30-12.30 Alois Kneip Tim Hulshof / Bartek Knapik Ronald Meester 
12.30-13.30 lunch lunch lunch
13.30-14.30 --- ---
14.30-15.30 Ronald Meester Ronald Meester
15.30-16.30 Alois Kneip Alois Kneip
16.30-17.00 tea tea
17-18 Robert Fitzner / Lidia Burzala  Alois Kneip 
18.30 dinner dinner

Abstracts and Titles

Alois Kneip, Univ Bonn, Dld
Functional data analysis
Functional data analysis is a new and rapidly developing area of statistics which deals with the analysis of data representing samples of curves. An example in finance is the analysis of implied volatility functions recorded for a number of different trading days. Functional data analysis is a collection of statistical techniques answering questions like, "what are the main ways in which curves vary from one trading day to another?" The lectures will present some basic concepts in this area. Special attention will be devoted to functional regression.

Ronald Meester, VU
In this lectures I will introduce the basic abelian sandpile, and study its behaviour, in particular its stationary distribution. Then we discuss some variations, like the Manna sandpile, the Zhang sandpile and the continuous abelian sandpile models. We will also spend some time on infinite volume versions of some of these models. I will start from scratch.

PhD students

Robert Fitzner
Lace expansion for dummies
After the first contact to the lace expansion most people are terrified by the involved analysis and the sheer amount of neccessary notation. This talk at the AI0-meeting should give a small and easy introduction to this pertubation technique. We will see how the lace expansion was used to prove that for dimension d bigger then 4 the self-avoiding walk on the Zd-lattice has the same mean-field behavoir as the simple random walk. And how this can be used to show that the self-avoiding walk, when properly scaled, converge to Brownian Motion.

Lidia Burzala
Estimation of human dose response curve based on the allometric scaling rule
In this talk we introduce two models for estimating human dose response curve based on the allometric scaling rule. These models are an example of Shape Invariant Models. Estimation of the human dose response curve involves estimation of a common model function (archetype) and a scaling factor. We consider a parametric and a shape constrained nonparametric approach for modeling the archetype function. The asymptotic properties of these estimators will be discussed.

Zhe Guo
Hammersley's process on the circle and its longest way
Hammersley’s process (HP) is an interacting particle system which is introduced firstly in 1972 by Hammersley J.M. and developed in recent years, we’ve already have some interesting results on the line.
In this talk, I will introduce principally the specific HP on the circle and show you some basic speed theorems of the particles and second class particles which start from the Uniform distribution in this model; moveover, one result of the longest way will be shown by constructing two related interacting systems and the almost sure convergence of the second class particle.

Henk Don
Algebraic differences of random Cantor sets
Suppose we have two subsets A and B of the unit interval and we consider the algebraic difference set A-B, containing all numbers that can be written as the difference of a number in A and a number in B. Does this difference set contain an interval? We will try to answer this question for a special choice of A and B: random Cantor sets. The construction of those random Cantor sets will be explained and some recent results will be discussed.

Bartek Knapik
Bayesian inverse problems
We consider the problem of estimating an object f that we observe not only with some noise, but also modified by some operator K. These so-called inverse problems have been studied extensively in the literature over past years. In this talk we present Bayesian methodology for solving inverse problems and compare it to well-known frequentist results. We also consider estimating the value of a linear functional of the object f and present the Bernstein-von Mises type result that links Bayesian methodology and ML-estimation.

Tim Hulshof
The incipient infinite cluster in high-dimensional percolation
In this talk I will discuss some properties of high-dimensional percolation at criticality. Specifically, I will discuss the volume of the intersection between the critical cluster and a ball and show how this depends on specific properties of the model. I will also discuss similar properties of the incipient infinite cluster.