17th Meeting of AiOs in Stochastics

18 - 20  MAY  2009

The seventeenth meeting of the AiOs (PhD students) in Stochastics in the Netherlands will take place from 18 - 20  May 2009. 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 Mike Keane and Aad van der Vaart. 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 220 euros. See the registration form for specifics on payment.

Further Information
For further information contact the organizers Ronald Meester and Aad van der Vaart, or Maryke Titawano for practical matters.

Detailed Program

Monday Tuesday Wednesday
8-9 breakfast breakfast
9-10 Aad van der Vaart Aad van der Vaart
10.00-10.30 coffee coffee
10.30-11.30 arrival/coffee Mike Keane Mike Keane
11.30-12.30 Aad van der Vaart Tim van Erven / René de Jonge Mike Keane 
12.30-13.30 lunch lunch lunch
13.30-14.30 --- ---
14.30-15.30 Mike Keane Mike Keane
15.30-16.30 Aad van der Vaart Aad van der Vaart
16.30-17.00 tea tea
17-18 Birgit Witte/ PhD student  Andras Balint / Matthijs Joosten 
18.30 dinner dinner

Abstracts and Titles

Mike Keane, Wesleyan Univ
Once Reinforced Random Walks on Lines and Ladders
In this series of lectures I shall begin by reviewing the theory of recurrence and transience for simple random walks on locally finite, countably infinite graphs. The notion of once reinforced random walks makes sense in this setting, and after its introduction and discussion, an interesting open problem concerning the recurrence-transience dichotomy will be discussed and a new partial solution will be presented. Subsequently, once reinforced random walk on the nearest neighbor graph whose vertices are integers will be treated; I'll give two proofs of the recurrence of these walks for any value of the reinforcement parameter. Finally, a proof of recurrence for the ladder of height two (a strip of height two in the discrete plane, with nearest neighbor edges) due to T. Sellke will be discussed, and the open problem of recurrence for strips of larger heights, together with partial results of Sellke, Vervoort, and Feiden will be presented. If time permits I shall show that such walks on trees (except for Z) are transient under any reinforcement - a result due to Durrett, Kesten, and Limic. The lectures will be accessible to a broad mathematical audience, and will not require any specialized knowledge in stochastics; however, mathematical maturity at the graduate level is probably necessary for understanding the statements and arguments.

Aad van der Vaart, VU
Entropy methods in statistics
Metric entropy was introduced by Kolmogorov in the 1960s, and is a measure of complexity of a metric space. It is defined as the logarithm of the minimum number of balls of a given radius needed to cover a metric space, as function of the radius. In statistics it is a useful concept to measure the complexity of a statistical model, which permits to describe the precision of estimation. In these lectures we discuss metric entropy and some of its variations, in abstract terms and as applied to examples, such as Holder or Besov spaces. Next we discuss three types of applications in statistics. The first is the abstract approach to estimation by Le Cam and Birge, who first introduced the concept in statistics. The second application concerns minimum contrast estimation, including Vapnik-Cervonenkis theory and machine learning methods, and is closely linked to empirical process theory. The third is in the derivation of rates of contraction of posterior distributions in nonparametric Bayesian statistics.

PhD students
Andras Balint: Confidence intervals for the critical values in the DaC model.
Tim van Erven: The Catch-Up Phenomenon in Bayesian Model Selection and Prediction.
René de Jonge
: Adaptive nonparametric Bayesian regression using location-scale mixture priors.
Matthijs Joosten: Scaling limits in 2D-percolation.