## Invited tutorials at ISIPTA '03 on July the 14th 2003

On the day July the 14th 2003, prior to the start of the technical sessions (on the days 15--17), there will be five invited tutorials of 75 minutes each. The tutorials will provide a gentle introduction to a wide range of important subject matters in imprecise probability, from foundational questions to models with potential for great impact on the application side. The tutorials are included in the (regular or student) registration fee. You are kindly invited to participate.

### TUTORIAL 1

SPEAKER: Prof. Gert de Cooman, Ghent University, Belgium.
TITLE: A gentle introduction to imprecise probability models and their behavioral interpretation.
SLIDES: Get a pdf file with tutorial slides.
ABSTRACT:
The tutorial will introduce basic notions and ideas in the theory of imprecise probabilities. It will highlight the behavioural interpretation of several types of imprecise probability models, such as lower previsions, sets of probability measures and sets of desirable gambles; as well as their mutual relationships. Rationality criteria for these models, based on their interpretation, will be discussed, such as avoiding sure loss and coherence. We also touch upon the issues of conditioning, and decision making using such models.

### TUTORIAL 2

SPEAKER: Dr. Jean-Marc Bernard, Universitè Paris 5 & CNRS, France.
TITLE: Imprecise Dirichlet model for multinomial data.
SLIDES: Get a pdf file with tutorial slides.
ABSTRACT:
The Imprecise Dirichlet Model (IDM) is a model for statistical inference and coherent learning from multinomial data, and, more generally, for categorical data under various sampling models. The IDM was proposed by Walley (1996, JRSS B, 58 No.~1, 3--57) as an alternative to other objective approaches to inference, since it aims at modeling prior ignorance about the unknown chances $\theta$ of a multinomial process. The IDM is an imprecise probability model in which prior uncertainty about $\theta$ is described by a set of prior Dirichlet distributions. The set of priors is updated, by the means of Bayes' theorem, into a set of Dirichlet posterior distributions, so that the IDM can be viewed as a generalization of Bayesian conjugate analysis. As in any imprecise probablity model, inferences can be summarized by computing upper and lower probabilities for any event of interest. The IDM induces prior ignorance (characterized by maximally imprecise probabilities) about $\theta$ and many other derived parameters. The IDM has many advantages over alternative objective inferential models. It satisfies several general principles for inference which no other model jointly satisfies: symmetry, coherence, likelihood principle, and other desirable invariance principles. By conveniently chosing its hyperparameter $s$ (which determines the extent of imprecision), the IDM can be tailored to encompass alternative objective models, either frequentist or Bayesian. After presenting the IDM, both from the parametric viewpoint (inferences about $\theta$) and the predictive viewpoint (inferences about future observations), we shall review its major properties, and then focus on applications of the IDM for various statistical problems.

### TUTORIAL 3

SPEAKER: Prof. Charles F. Manski, Northwestern University, USA.
TITLE: Partial identification of probability distributions.
SLIDES: Get a pdf file with tutorial slides.
ABSTRACT:
This tutorial exposits elements of the research program presented in Manski, C., Partial Identification of Probability Distributions, Springer-Verlag, 2003. The approach is deliberately conservative. The traditional way to cope with sampling processes that partially identify population parameters has been to combine the available data with assumptions strong enough to yield point identification. Such assumptions often are not well motivated, and empirical researchers often debate their validity. Conservative analysis enables researchers to learn from the available data without imposing untenable assumptions. It also makes plain the limitations of the available data. Whatever the particular subject under study, the approach follows a common path. One first specifies the sampling process generating the available data and ask what may be inferred about population parameters of interest in the absence of assumptions restricting the population distribution. One then asks how the (typically) set-valued identification regions for these parameters shrink if certain assumptions (e.g., statistical independence or monotonicity assumptions) are imposed. Major areas of application include regression with missing outcome or covariate data, analysis of treatment response, and decomposition of probability mixtures.

### TUTORIAL 4

SPEAKER: Prof. Fabio G. Cozman, University of Sao Paulo, Brazil.
TITLE: Graph-theoretical models for multivariate modeling with imprecise probabilities.
SLIDES: Get a pdf file with tutorial slides.
ABSTRACT:
Markov chains, Markov fields, Bayesian networks, and influence diagrams are often used to construct standard probability models. These models share the property that they are based on graphs. We ask, how do these models behave when probability values are imprecise? What are the independence concepts at play, and what are the computational tools that we could use to manipulate the resulting models? This tutorial will describe results that have been obtained in recent years, mostly in the field of artificial intelligence, concerning graphical models and imprecise probabilities. Most results have focused on directed acyclic graphs, with interesting applications ranging from classification to sensitivity analysis in expert systems.

### TUTORIAL 5

SPEAKER: Prof. Sujoy Mukerji, Oxford University, UK.
TITLE: Imprecise probabilities and ambiguity aversion in economic modeling.
PAPER: Get a pdf file with the paper.
ABSTRACT:
The talk will have, roughly, two parts. The first part will give an introductory account of decision theoretic frameworks, useful in economic modeling, that incorporate the hypothesis that cognitive limitations may imply that decision makers' beliefs are represented by imprecisie probabilities. The second part will discuss some examples of economic modeling that apply such frameworks.