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.

**Programme**

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.

**Location**

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

**Registration**

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.

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 |

**Alois Kneip, Univ Bonn, Dld**

*Functional data analysis*

Abstract:

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**

Abstract:

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*

Abstract:

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*

Abstract:

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*

Abstract:

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*

Abstract:

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*

Abstract:

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*

Abstract:

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.