Monday 16 July 2007

TUTORIAL I 09:00 - 10:35

Risk analysis: rough but ready tools for calculations under variability and uncertainty

Scott Ferson

Risk analysis is widely used in many disciplines to quantify risks or expectations in the face of pervasive variability and profound uncertainty about both natural and engineered systems. Although most analyses today are still based on point estimates, awkward qualitative assessments, or probabilistic calculations employing unwarranted assumptions, the methods of imprecise probability hold great promise for allowing analysts to develop quantitative models that make use of the knowledge and data that are available but do not require untenable or unjustified assumptions or simplifications. This tutorial will introduce some of the methods that are easiest to make calculations with, including probability bounds analysis, Dempster-Shafer evidence theory, and interval statistics, and will show how they can be used to address the basic problems that risk analysts face: not knowing the input distributions, not knowing their correlations, not being sure about the model itself, or even which variables should be considered. We suggest that these tools constitute a practical uncertainty arithmetic (and logic) that can be widely deployed for lots of applications. Of course, not all problems can be well solved by these relatively crude methods. Examples requiring fuller analyses with the methods of imprecise probability are described.

TUTORIAL II 11:00 - 12:35

An introduction to the theory of coherent lower previsions

Enrique Miranda

In this tutorial, I introduce the main elements of Peter Walley's theory of coherent lower and upper previsions. I review the notions of avoiding sure loss and coherence, and the representation of coherent assessments in terms of sets of linear previsions and sets of almost-desirable gambles. Then, I turn to the notion of natural extension, and give its expression under any of these three equivalent representations. Finally, I study how to update assessments in a coherent way, presenting the main facts about conditional lower previsions.

TUTORIAL III 14:00 - 15:35

Generalized information theory

George J. Klir

A research program whose objective is to study the dual concepts of information-based uncertainty and uncertainty-based information in all their manifestations was introduced in the early 1990s under the name "generalized information theory2 (GIT). The purpose of this tutorial is to introduce conceptual boundaries within which GIT operates and a comprehensive overview of principal results that emerged from GIT. As in classical information theory, uncertainty is the primary concept and information is defined in terms of uncertainty reduction. GIT is based on a two-dimensional expansion of classical information theory. In one dimension, additive probability measures of classical information theory are expanded to various types of nonadditive measures. In the other dimension, the theory of classical sets, within which probability measures are formalized, is expanded to the various theories of fuzzy sets. Each choice of a particular set theory and a particular measure theory defines a particular information theory. The full development of any of these information theories requires that issues at each of the following four levels be adequately addressed: (1) an uncertainty function, u, of the theory be formalized in term of appropriate axioms; (2) the calculus for dealing with function u be properly developed; (3) a justifiable functional, U, be determined by which the amount of relevant uncertainty (predictive, prescriptive, diagnostic, etc.) associated with function u is measured; and (4) methodological aspects of the theory be developed by utilizing functional U as a measuring instrument. The tutorial is presented in two parts of approximately the same duration. An overall characterization of GIT is presented in the first part. After a brief overview of classical information theory, a general framework for formalizing uncertainty and the associated uncertainty-based information of any conceivable type is sketched. The various theories of imprecise probabilities that have already been developed within this framework are surveyed and some important unifying principles applying to these theories are introduced. The second part is devoted to the issues of measuring uncertainty and information in the various theories and to the methodological principles based on these measuring capabilities. The tutorial is concluded by a discussion of some open problems in the area of GIT. The tutorial is intended as a gentle introduction to the area of GIT, which is covered in a greater depth in the recent book "Uncertainty and Information: Foundation of Generalized Information Theory" by George J. Klir (Wiley-Interscience, 2006).

TUTORIAL IV 16:00 – 17:35

Decision theories for imprecise preferences and imprecise probabilities

Teddy Seidenfeld

This tutorial offers an overview of selected alternative decision theories designed for use with IP theory. The review begins with an examination of the kinds of rival decision theories that ensue when each of the familiar axioms of, for instance, Anscombe-Aumann Horse Lottery theory is relaxed to accommodate normal-form IP theory. From this base, further generalizations are considered, including: multi-agent decision making, extensive form IP theory, and several interesting considerations that attend problems with infinite decision structures.

Tuesday 17 July 2007

STATISTICAL REASONING AND DECISION MAKING I 08:45 - 10:25

Coherent choice functions under uncertainty (385)

Teddy Seidenfeld, Mark J. Schervish, Joseph B. Kadane

Finite approximations to coherent choice (425)

Matthias C. M. Troffaes

Luceños' discretization method and its application in decision making under ambiguity (327)

Michael Obermeier, Thomas Augustin

Minimax regret treatment choice with finite samples and missing outcome data (415)

Jörg Stoye

Linear regression analysis under sets of conjugate priors (445)

Gero Walter, Thomas Augustin, Annette Peters

APPLICATIONS 10:40 - 12:00

Uncertainty analysis in food engineering involving imprecision and randomness (21)

Cédric Baudrit, Arnaud Hélias, Nathalie Perrot

Predicting the next pandemic: An exercise in imprecise hazards (41)

Miķelis Bickis, Uģis Bickis

Imprecise probability methods for sensitivity analysis in engineering (317)

Michael Oberguggenberger, Julian King, Bernhard Schmelzer

Estimating probability distributions by observing betting practices (281)

Caroline Lynch, Donald Barry

COHERENCE AND NATURAL EXTENSION 14:30 - 16:30

Some results on imprecise conditional prevision assessments (31)

Veronica Biazzo, Angelo Gilio

Some bounds for conditional lower previsions (337)

Renato Pelessoni, Paolo Vicig

Coherence graphs (297)

Enrique Miranda, Marco Zaffalon

Enhancement of natural extension (253)

Igor Kozine, Victor Krymsky

Computing expectations with p-boxes: two views of the same problem (435)

Lev Utkin, Sébastien Destercke

Coherence and fuzzy reasoning (165)

Serena Doria

INVITED TALK I 16:50 - 18:00

Game-theoretic probability: Theory and applications

Glenn Shafer

Wednesday 18 July 2007

MARKOV PROCESSES + PSYCHOLOGICAL STUDIES 08:45 - 10:25

Multilinear and integer programming for Markov decision processes with imprecise probabilities (395)

Ricardo Shirota Filho, Fabio Gagliardi Cozman, Felipe Werndl Trevizan, Cassio Polpo de Campos, Leliane Nunes de Barros

Regular finite Markov chains with interval probabilities (405)

Damjan Škulj

Conditioning in chaotic probabilities interpreted as a generalized Markov chain (365)

Leandro Chaves Rêgo

Human reasoning with imprecise probabilities: Modus ponens and denying the antecedent (347)

Niki Pfeifer, Gernot D. Kleiter

On the explanatory power of indeterminate probabilities (117)

Horacio Arlo Costa, Jeffrey Helzner

FOUNDATIONS 10:40 - 13:00

The logical concept of probability: Foundation and interpretation (455)

Kurt Weichselberger

Scoring rules, entropy, and imprecise probabilities (307)

Robert Nau, Victor Richmond Jose, Robert Winkler

On coherent immediate prediction: Connecting two theories of imprecise probability (97)

Gert de Cooman, Filip Hermans

An extension of chaotic probability models to real-valued variables (193)

Pablo I. Fierens

BELIEF FUNCTIONS AND RANDOM SETS 14:30 - 16:30

An independence concept under plausibility function (287)

Marcello Mastroleo, Barbara Vantaggi

Independence concepts in evidence theory (125)

Inés Couso

Compositional models of belief functions (243)

Radim Jiroušek, Jiřina Vejnarová, Milan Daniel

Constructing predictive belief functions from continuous sample data using confidence bands (11)

Astride Aregui, Thierry Denoeux

Multiparameter models: Probability distributions parameterized by random sets (183)

Thomas Fetz

On various definitions of the variance of a fuzzy random variable (135)

Inés Couso, Didier Dubois, Susana Montes, Luciano Sánchez

INVITED TALK II 16:50 - 18:00

In the realm of probability: Limits to standard probability

Terrence Fine

Thursday 19 July 2007

CREDAL NETS + PROBABILISTIC LOGIC 08:45 - 10:25

Credal networks for military identification problems (1)

Alessandro Antonucci, Ralph Brühlmann, Alberto Piatti, Marco Zaffalon

Credal nets with probabilities estimated with an extreme Imprecise Dirichlet Model (57)

Andrés Cano, Manuel Gómez Olmedo, Serafín Moral

Inference in credal networks through integer programming (145)

Cassio Polpo de Campos, Fabio Gagliardi Cozman

Climbing the hills of compiled credal networks (213)

Rolf Haenni

Qualitative and quantitative reasoning in hybrid probabilistic logic programs (375)

Emad Saad

GENERAL ASPECTS 10:40 - 12:00

Comparative probability orders and the flip relation (67)

Marston Conder, Dominic Searles, Arkadii Slinko

Measuring uncertainty with imprecision indices (47)

Andrey Bronevich, Alexander Lepskiy

Relating practical representations of imprecise probabilities (155)

Sébastien Destercke, Didier Dubois, Éric Chojnacki

On σ-additive robust representations of convex risk measures for unbounded financial positions in the

presence of uncertainty about the market model (263)

Volker Krätschmer

STATISTICAL REASONING AND DECISION MAKING II 14:30 - 16:10

Data-based decisions under imprecise probability and least favorable models (203)

Robert Hable

Distributions over expected utilities in decision analysis (175)

Love Ekenberg, Mikael Andersson, Mats Danielson, Aron Larsson

Information processing under imprecise risk with the Hurwicz criterion (233)

Jean-Yves Jaffray, Meglena Jeleva

Quantile-filtered Bayesian learning for the correlation class (223)

Hermann Held

Updating and testing beliefs: An open version of Bayes' rule (271)

Elmar Kriegler

PREDICTIVE INFERENCE AND PRIOR IGNORANCE 16:30 - 17:50

Jury size and composition - a predictive approach (87)

Frank P. A. Coolen, Brett Houlding, Steven G. Parkinson

Multinomial nonparametric predictive inference with sub-categories (77)

Frank P. A. Coolen, Thomas Augustin

Immediate prediction under exchangeability and representation insensitivity (107)

Gert de Cooman, Enrique Miranda, Erik Quaeghebeur

Learning about a categorical latent variable under prior near-ignorance (357)

Alberto Piatti, Marco Zaffalon, Fabio Trojani, Marcus Hutter