13th Meeting of AiOs in Stochastics

The thirteenth meeting of the AiOs (PhD students) in Stochastics in the Netherlands will take place from 9 - 11  May 2005. This meeting is organized by the AiO Network Stochastics and is supported by the research schools MRI and Stieltjes Institute. 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 Jeff Steif and Jon Wellner. 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 130 euros for aios. The total fee is 180 euros for all others. 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
 

Abstracts and Titles

Jeff Steif
An introduction to particle systems and stochastic domination: percolation, Ising models and the contact process.

Abstract
This lecture series will begin with the topic of percolation and the notions of phase transition and critical value. (A phase transition is a phenomenon where a system exhibits two vastly differing behavior depending on the choice of a key parameter value.) In particular, we will prove the existence of a phase transition for percolation. We will then go on to study so-called Markov random fields and concentrate on a particular example called the Ising model which has its origin in statistical physics. We will show the surprising fact that one can have two Markov random fields with the same conditional probabilities given the outside; this would be the analogue of an irreducible, aperiodic Markov chain having more than one stationary distribution which is of course false. Also, we will introduce the contact process and describe some of its basic features. Again, in this model, there will be a phase transition. A look at the contact process will provide the student with an introduction to the vast field of "interacting particle systems". "Stochastic domination" is an important tool in the above subjects. Should time permit, I will present some new results obtained in joint work with Tom Liggett concerning stochastic domination and the Ising and contact models.

Jon Wellner
Nonparametric Estimation under Shape Restrictions.

Abstract
In many statistical problems there is some knowledge of the shape of the functions available ``a priori'': monotonicity, convexity, number of modes, or ``degree of oscillation'' are examples of this type of information. This type of restriction becomes most interesting in the context of nonparametric estimation when the parameters to be estimated are functions and the other aspects of the unknown function beyong ``shape'' are arbitrary. Models for statistical problems involving shape restrictions often arise via (nonparametric) mixture models.
In this course we will discuss some of commonly occurring shape constraints, and examples of problems in which they occur.
We will focus on likelihood methods for estimation and testing, but will briefly mention some of the other methods that have been proposed.
The methods will be evaluated via large sample theory, including discussion of limiting distributions, construction of asymptotic minimax lower bounds, and attainment of these bounds. Algorithmic aspects will not be emphasized, but will be discussed briefly.