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.

**Programme**

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.

**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 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.

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 |

**Mike Keane, Wesleyan Univ**

*Once Reinforced Random Walks on Lines and Ladders*

Abstract:

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*

Abstract:

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**: