Info-Gap Theory and Imprecision - Workshop at Durham: 13-14 July 2007

The Department of Mathematical Sciences, Durham University, organizes a workshop on `Info-Gap Theory and Imprecision', on Friday 13 July and Saturday 14 July 2007. The Friday will be a day of lectures, the Saturday will be used for (mostly informal) discussions aimed at bringing expertise together and considering important research problems. If you want more information, please contact one of the organisers (see bottom of page). Everyone is welcome to attend, one or both days! Please note that Yakov Ben-Haim will also give a general lecture on Info-Gap Theory, entitled `Why More is Less: Info-Gap Explanation for Robust-Satisficing Behavior', at Durham on Thursday 12 July at 16.00 - all are welcome (see below for more details).

Details

The workshop will take place in lecture room CM221 in the Department of Mathematical Sciences, Durham. This is number 15 on the Map.

More information about travelling to Durham can be found Travel Info, whilst information on suitable accommodation (en-suite rooms, B&B, in Durham colleges) is available Accommodation Info. All colleges offer suitable accommodation, if you wish a recommendation then we would suggest Collingwood College.

As Durham is a particularly beautiful small city (its Cathedral and Castle are a UNESCO World Heritage Site), with all attractions at short walking distance from the University and its colleges, this is an ideal opportunity to also spend some time as a tourist - see Tourist Info.

The timing of this workshop makes is particularly suitable for researchers who also participate at ISIPTA'07 - the Fifth International Symposium on Imprecise Probability: Theories and Applications, in Prague (16-19 July), for more information see the webpage: ISIPTA'07. There are suitable flights from Newcastle Airport to Prague (e.g. EasyJet).

Friday 13 July - Research Presentations

Currently, there are 7 talks scheduled, each 30 minutes including 5 minutes for discussion. If you wish to participate and also give a presentation, please let the organisers know as soon as possible (we can include one or two more talks).

Preliminary Programme

The following speakers will present work with the titles as given. Some abstracts are included further down the webpage.

Saturday 14 July - Informal Research Discussions

Following from topics mentioned and discussed on Friday, we will have some group discussions, and plenty of time for discussions in small groups, aimed at bringing together problems, ideas and possible solutions. This day will have mostly an informal nature, and is likely to start at about 10.00 and finish at about 16.00. If you attend this workshop, and do not wish to give a full lecture but still would like to raise some problems you are working on or are interested in, you are welcome to give a brief presentation (about 5 minutes perhaps, we do not want lectures on a Saturday!) on this day to also feed into the discussions.

Thursday 12 July - General Lecture by Yakov Ben Haim

On Thursday 12 July, Yakov Ben Haim will give a research presentation at the Durham Institute of Advanced Study, aimed at introducing some aspects of Info-Gap Theory to a wide audience. This lecture, entitled `Why More is Less: Info-Gap Explanation for Robust-Satisficing Behavior', will take place at 16.00, also in room CM221 in the Department of Mathematical Sciences.

Abstract:

In this talk we discuss the questions: why, and when, and in what form, a satisficing strategy is a better bet for survival, than a strategy which uses the best available information in attempting to optimize the outcome. We discuss theorems asserting that, under severe uncertainty, a robust-satisficing decision has a better probability of survival than a best-model outcome-optimizing decision. These theorems are based on non-probabilistic info-gap decision theory, which provides a quantification of Knightian uncertainty. These theorems are applicable to Bayesian mixing of two models, allocation between a risky and a risk-free asset, foraging behavior, explaining Ellsberg's paradox, satisfying multiple requirements, forecasting in dynamical systems, and managing exogenous uncertainties.

Abstracts of Friday's Talks

Jonathan Lawry (Bristol) - Imprecise Linguistic Rules for High-Level Qualitative and Quantitative Modelling

This talk will outline the use of label semantics for imprecise linguistic rules providing high-level qualitative models of complex systems. The label semantics framework gives a probabilistic interpretation of the uncertainty resulting from the use of vague or imprecise linguistic descriptions in high-level models. As such it is straightforward to integrate with other sources of uncertainty in data, to provide a representation framework for new learning algorithms which generate linguistic models from data mining. These relatively transparent models allow for a qualitative understanding of underlying relationships underlying the data, in addition to giving accurate quantitative predictions.

Malcolm Farrow (Newcastle) & Michael Goldstein (Durham) - Experimental design with imprecise utility hierarchies

Imprecise multi-attribute utility may be constructed in a similar way to imprecise probability by considering our partial ordering over preferences on attributes. This leads naturally to the notion of an imprecise utility hierarchy, representing the imprecision in the trade-off between the various attributes of a decision problem. We describe the analysis of such imprecise hierarchies and show how this formulation may be employed when balancing gains in information against the various costs involved in problems of experimental design.

Yakov Ben-Haim (Haifa) - Why we design to spec: info-gap explanation for satisficing design requirements

Why does the engineering profession commonly specify performance requirements as inequality constraints, rather than specifying constrained-optimal design? Hammurabi's Code of Law imposed extreme penalties for design failures, providing strong incentives for engineers to meet design specs. Engineers still bear legal liability for design failure, though less severely than in ancient Babylonia. So why do engineers satisfice, rather than optimize, performance requirements? In this talk we discuss theorems asserting that, under severe uncertainty, a robust-satisficing decision has a better probability of survival than a best-model outcome-optimizing decision. These theorems are based on non-probabilistic info-gap decision theory, which provides a quantification of Knightian uncertainty. We discuss a stylized design problem, a fault-detection example, and forecasting subject to surprises.

Pauline Coolen-Schrijner & Frank Coolen (Durham) - Imprecision in nonparametric predictive inference

Nonparametric Predictive Inference (NPI) has been developed as a statistical approach based on limited structural assumptions, with uncertainty quantified via imprecise probabilities. In NPI, imprecision, which is the difference between the upper and lower probabilities for an event, depends on several factors, including the number of observations available, the inference horizon, grouping and censoring of data. In this talk, we highlight the way in which imprecision depends on such factors via several examples, and we pose some related questions about imprecision.

Graeme Manson (Sheffield) - Evidence-based damage classification for an aircraft structure

There has been a considerable amount of work on the use of neural networks for damage location and quantification. This work usually implicitly assumes a probabilistic basis for the classification. Other theories of uncertainty, perhaps with the exception of fuzzy set theory, have been largely unexplored in the context of damage identification. The object of this paper is to design a damage location system based on the Dempster-Shafer theory of evidence. The DS classifier is also implemented in this case by a neural network. The approach is demonstrated on a case study on the location of damage on an aircraft. The results are compared with previous results obtained within the probabilistic framework.

Matthias Troffaes (Durham) - On a unification of regular and natural extension

In this talk I will discuss issues with inference when conditioning on events that have lower probability zero. Such events occur commonly in practice, and within the traditional theory, natural extension leads to vacuous (i.e. entirely non-informative) inferences. A commonly used solution to circumvent this problem is called regular extension. I will show that in many cases the inferences may be too informative using regular extension. Therefore I suggest another alternative, based on non-Archimedean probability, that can produce non-vacuous inferences, yet avoiding some of the problems identified with regular extension.

Organisation:

Frank Coolen - e-mail: Frank.Coolen@durham.ac.uk

Pauline Coolen-Schrijner - e-mail: Pauline.Schrijner@durham.ac.uk

Matthias Troffaes - e-mail: Matthias.Troffaes@durham.ac.uk

Last revision: 05/07/07