Selected Lectures: Winter Term 2009/10

Advanced Processor Architecture

Prof. Dr. Hans-Joachim Wunderlich

Colloquium Theoretical Chemistry

Prof. Dr. H.-J. Werner, Prof. Dr. H. Stoll, Prof. Dr. G. Rauhut, Jun.-Prof. Dr. J. Kästner

Computational Fracture Mechanics

Jun.-Prof. Christian Linder

Coupled problems and numerical solution strategies

JP Oliver Roehrle, Ph.D.

ICP-Kolloquium: Physik und Computeranwendungen

Prof. Rudolf Hilfer, Prof. Christian Holm

Parameter Identification Methods and Experimental Mechanics

Björn Kiefer, Ph.D.

Stochastic and Statistical Tools in Simulation Technology

Jun.-Prof. Wolfgang Nowak

(adaptive, depending on participants) - Marginal, joint and conditional probability distributions, Bayes theorem - Measures for uncertainty and information - Maximum likelihood and Bayesian parameter estimation - Model testing, model selection, parsimony and model averaing - Subjectivity and objectivity in stochastic assumptions - Convergence analysis of stochastic simulation methods - Optimal design of experiments, philosophy of experiments

Vorlesung Modellreduktion

Jun.-Prof. Dr. B. Haasdonk

What is probability?

Eckhart Arnold

In this seminar we are going to examine what it means to say that something is possible or probable. Basically, there exist three different interpretations of probability: 1) Subjective Probability, where "probability" means the degree or the strength of a personal belief that something is the case or is going to happen. 2) Frequency Theory, where the probability is assumed to merely express the frequency of a certain property; e.g. the probability of dying from swine flu when infected is simply the frequency of death cases within the group of infected persons. 3) Propensity theories, where the probability is in some way or other assumed to be an objective property of single events.   In the seminar we will discuss the merits and disadvantages of each of these interpretations of the notion of probability. Furthermore, we will examine the relations between these interpretations, i.e. in how far they must be considered mutually exclusive or complementary to each other. Finally, we will discuss the relation between probability and decision theory. The most important question here is, in how far any of these concepts of probability is able to express the different degrees of insecurity that we have to face in decision making.   A previous knowledge of the mathematical probability calculus (on which all of the probability interpretations that will be discussed in the seminar rest) is recommendable but not required. We will briefly review the basics of the mathematical probability calculus in the first sessions of the seminar.

Donald Gillies: Philosophical Theories of Probability, New York / London 2000. Michael D. Resnik: Choices. An Introduction to Decision Theory, 8th reprint, Minneapolis / London, 2008. Leonard J. Savage: The Foundations of Statistics, 2nd ed., New York 1972. Karl Bosch: Elementare Einführung in die Wahrscheinlichkeitsrechnung, 7. Aufl., Braunschweig 1999.