[up]Department of Mathematics

The 24th Finnish Summer School on Probability Theory

The 24th Finnish Summer School on Probability Theory will be arranged at the Mukkula conference center in Lahti from June 3rd to June 7th, 2002. The course program is mainly made up of four series of lectures, about 6 h each. A couple of lectures by some of the course attendants may also be held. For those who want to get credit (2 credit units according to the Finnish system) for Professor Winkler's course in Image Analysis, an examination will be arranged. The school, which is arranged by the Finnish Graduate School in Stochastics, is mainly financed by the Academy of Finland through the Rolf Nevanlinna institute.

The venue is the Mukkula summer hotel.

The summer school begins on Monday June 3rd at 12 noon with lunch. The school ends on Friday June 7th around 1 p.m.

The course fee includes course material, lodging and lunches from Monday to Friday. Accommodation will be reserved in the summer hotel (Mukkulan kesähotelli). The fee is 210 € for accomodation in a single room and 165 € per person for accomodation in a double room. The payment is made on location in Lahti. Please mention at the hotel reception if you wish to have a special diet or if you have other special wishes. Registrations are due by May 10th 2002.

Welcome to Lahti!

Göran Högnäs

Addresses:

  • Åbo Akademi University, Department of Mathematics, 20500 Åbo
  • E-post: mateweb@abo.fi, ghognas@abo.fi
  • Telefax: +358 2 215 4865
  • Telefon: +358 2 215 4372 (Halldorsdottir), +358 2 215 4224 (Högnäs)

    • Speakers:

    Course descriptions:

    Pierre del Moral: Genealogical and Interacting Particle Approximations of Feynman-Kac Formulae with Applications

    This lecture focuses on interacting particle systems and genealogical tree based methods for solving numerically a class of Feynman-Kac formulae arising in the study of certain parabolic differential equations, physics, biology, evolutionary computing, nonlinear filtering and elsewhere. We give a short "exposè" of the mathematical theory that is useful for analyzing the convergence of such genetic-type particle models including law of large numbers, increasing propagation of chaos, large deviations principles, fluctuations, empirical process theory as well as semigroup techniques and limit theorems for processes.

    An important part of this course concerns the applications to non linear filtering/smoothing and path estimation of signals, directed polymers simulations, exit times and rare event analysis as well as spectral analysis of Schrödinger operators.


    Sidney Resnick: Heavy Tail Analysis with Applications to Data Network Modeling & Finance Heavy tail analysis intersects extreme value theory to provide a set of tools for probabilistic and statitistical analysis of many systems not following the standard, classical assumptions of independence and short tails. Data networks and finance offer two fascinating, if potentially frustrating, settings for many of these techniques to be applied. We survey some of the basic models and statistical techniques for fitting the models. We point out some of the shortcomings in the models and in the statistical techniques. The required range of techniques is broad. The ability to contribute in internet time is questionable. Some new modeling attempts are described.
    Edward J. Wegman: Data Visualization: Methods, Tools, and Environments Exploratory data analysis has evolved into a broad interdisciplinary field, bringing together elements of computer graphics, high-dimensional geometry, virtual reality, and data mining. This course will explore elements of all of these topics and is intended to synthesize them into a coherent approach to exploratory analysis. Geometric methods enter not only as a component of computer graphics, but also as an underpinning to understanding visually presented structures in high dimensions. Elements of computer graphics, especially lighting and rendering models, transparency, and stereoscopic methods, play a crucial role in modern graphical exploratory analysis. Virtual reality systems not only exploit more fully the capability of the human visual system, but also provide more comfortable environments for group interactions. Data mining has generally the same goals as exploratory data analysis, i.e. uncovering previously unknown structure and relationships in the data, but focuses on coping with data set sizes well beyond those normally encountered in traditional statistical analysis. Our course reviews all of these topics with the goal of data visualization in mind.
    G. Winkler, F. Friedrich: An Introduction to Bayesian Imaging and MCMC Methods

    Part I. Bayesian Image Analysis: Introduction

    1. The Bayesian Paradigm
        1.1 Warming up for Absolute Beginners
        1.2 Images and Observations
        1.3 Prior and Posterior Distributions
        1.4 Bayes Estimators
    2. Cleaning Dirty Pictures
        2.1 Boundaries and their information content
        2.2 Towards piecewise smoothing
        2.2 Boundary Extraction
    3. Random Fields
        3.1 Markov Random Fields
        3.2 Gibbs Fields and Potentials

    Part II. The Gibbs Sampler and Simulated Annealing

    4. Markov Chains: Limit Theorems
        4.1 Preliminaries
        4.2 The Contraction Coefficient
        4.3 Homogeneous Markov Chains
        4.4 Exact Sampling
        4.5 Inhomogeneous Markov Chains
        4.6 A Law of Large Numbers for Inhomogeneous Chains
    5. Gibbsian Sampling and Annealing
        5.1 Sampling
        5.2 Simulated Annealing
    6. Remarks and Short Introductions
        6.1 The ICM Algorithm
        6.2 Exact MAPE Versus Fast Cooling
        6.3 Metropolis Algorithms: An Overview
        6.4 Parallel Algorithms

    Part III. Texture Analysis: Demonstration

    Part IV. Parameter Estimation

    7. Maximum Likelihood Estimation:Some Theory
    8. Demonstration

    Part V. Practical Execises

    Here are some links related to the Summer School

    Updated 27.03.02 by mateweb@abo.fi