Dear list members, the slides of the following tutorials can be downloaded from the web site of the 3rd International Symposium on Imprecise Probabilities and Their Applications:
Jean-Marc Bernard: Imprecise Dirichlet model for multinomial data (http://www.sipta.org/~isipta03/jean-marc.pdf). 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 probability 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 choosing 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. Gert de Cooman: A gentle introduction to imprecise probability models and their behavioral interpretation (http://www.sipta.org/~isipta03/gert.pdf). 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. Fabio G. Cozman: Graph-theoretical models for multivariate modeling with imprecise probabilities (http://www.sipta.org/~isipta03/fabio.pdf). 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. Charles F. Manski: Partial identification of probability distributions (http://www.sipta.org/~isipta03/charles.pdf). 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. Sujoy Mukerji: Imprecise probabilities and ambiguity aversion in economic modeling (http://www.sipta.org/~isipta03/sujoy.pdf). 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 imprecise probabilities. The second part will discuss some examples of economic modeling that apply such frameworks. The slides of the following invited talks are also available: Terrence L. Fine, Theories of Probability: Some Questions about Foundations (http://www.sipta.org/~isipta03/terry.pdf). ABSTRACT: We consider some of the following questions and offer some thoughts but no answers. How do we recognize probabilistic reasoning and its armature of probability theory? How is the study of probabilistic reasoning distinguished from study of other forms of indeterminacy, imprecision, and vagueness? Methodology or theory? What counts as a theory of probability and what does not? Is there a unified concept of probability? Is probability fundamental or is it merely a convenient placeholder for a more detailed account? Can we judge ``adequacy'' (satisfaction, success) outside of the very methodology/theory of probability we are using? Is a pragmatic stance sufficient or merely defeatist? Is self-consistency sufficient or at most necessary? What are examples of domains, however small, and probability theories for them that are unproblematic? What are examples of conceptual frameworks or spaces within which to have this discussion? Irving J. Good, The Accumulation of Imprecise Weights of Evidence (http://www.sipta.org/~isipta03/jack.pdf). ABSTRACT: A familiar method for modeling imprecise or partially ordered probabilities is to regard them as interval valued. It is proposed here that it is better to assume a Gaussian form for the logarithm of the probabilities. To fix the hyperparameters of the Gaussian curve one could make judgements for the quartiles for example. The same comment applies for weights of evidence. The reason for this proposal is that when the pieces of evidence are statistically independent one has additivity and the addition of Gaussian curves is easy to perform. When the pieces of evidence are dependent, there is a more general additivity, or one might be able to allow for interactions of various orders. Possible applications would be to legal trials and to differential diagnosis in medicine, or even for distinguishing between two hypotheses in general. Patrick Suppes, Application of Nonmonotonic Upper Probabilities to Quantum Entanglement (http://www.sipta.org/~isipta03/patrick.pdf). ABSTRACT: A well-known property of quantum entanglement phenomena is that random variables representing the observables in a given experiment do not have a joint probability distribution. The main point of this lecture is to show how a generalized distribution, which is a nonmonotonic upper probability distribution, can be used for all the observables in two important entanglement cases: the four random variables or observables used in Bell-type experiments and the six correlated spin observables in three-particle GHZ-type experiments. Whether or not such upper probabilities can play a significant role in the conceptual foundations of quantum entanglement will be discussed. Best wishes, Marco Zaffalon ----------------------------------------- Dr. Marco Zaffalon Senior Researcher IDSIA Galleria 2 CH-6928 Manno (Lugano) Switzerland phone +41 91 610 8665 fax +41 91 610 8661 email mailto:[EMAIL PROTECTED] web http://www.idsia.ch/~zaffalon -----------------------------------------
