Programme
Day  Subject  Led by 

Mon 12 May  research presentations  
Tue 13 May  regression methods  Jochen Einbeck, Frank Coolen, and Gero Walter 
Wed 14 May  Markov theory  Damjan Skulj and Marco Cattaneo 
Thu 15 May  decision making  Matthias Troffaes and Robert Hable 
Fri 16 May  principles and methods of statistics  Frank Coolen and Thomas Augustin 
Monday Presentations
Time  Event/Speaker  Abstract 

10:00  Coffee  
10:20  Glenn Shafer  The Wiki of the online prediction group (Royal Holloway), and some open problems in probability theory. 
11:10  Sebastien Destercke  Relating independence notions of imprecise probability theory to event trees. There are currently two main approaches to probability theory that uses lower and upper expectations:
Walley's behavioural approach, and Shafer and Vovk's gametheoretic framework, where event trees
play a central role. De Cooman and Hermans have shown that these two approaches can be related to
each other, and they have introduced imprecise probability trees as a bridge between them, making a step
towards a more unified handling of uncertainty.
In this talk, we go a little step further into such a unification, by giving first results relating notion of
independence originating from Walley's behavioral theory to the notion of event trees independence
given by Shafer.
In the first part of the talk, we give an account of recent results showing that the notion of forward
irrelevance is equivalent to eventtree independence in particular event trees. We argue that, in a theory
of uncertain processes, the asymmetrical notion of epistemic irrelevance has a more important role to play
than its more involved and symmetrical counterpart called epistemic independence.
In the second part of the talk, we give some preliminary ideas as to how the more involved notion of epistemic independence could be related to event trees, and raise the issues of relating other structural judgments
such as permutability or exchangeability in event trees.
Results presented and discussed in this talk are the consequences of a joint work and of fruitful discussions with Gert de Cooman, most of them done during a two month stay at SYSTeM research group. References

12:00  Lunch  
14:00  Ian Vernon  Galaxies and imprecision. 
14:50  Carolin Strobl  Classification  An Overview over Standard and Credal Classification
Approaches with an Emphasis on Instability and Interpretability.
Classification trees are one representative out of a vast variety of
statistical classification techniques. While their nonparametric and
flexible recursive partitioning approach has added much to the
popularity of classification trees in many applied sciences, they
are known to be instable with respect to small changes in the
learning data and their variable selection criteria can be
artificially biased in favor of variables of certain types.
Different advancements of the standard classification tree methodology have been suggested to deal with the issue of instability, as well as the related issue of overfitting: The ensemble methods bagging and random forests have been suggested in the machine learning community and employ random sampling techniques to generate sets of classification trees. Another, more recent and thus less well known approach from this community is TWIX, where sets of classification trees are generated by splitting in additional optimal cutpoints. In the imprecise probabilities community, on the other hand, credal classification trees have been proposed, that employ an upper entropy approach for conservative split selection in order to avoid overfitting. The talk gives a short overview over these existing methods with an emphasis on the issues of interpretability and unbiased variable selection. For the TWIX approach an adaptive, datadriven split selection criterion is suggested, that turns out to be closely related to the Imprecise Dirichlet Model. With this criterion, additional cutpoints are selected in a datadriven way to create a set of trees, while the ensemble reduces to a single, interpretable tree when the partition is sufficiently stable. 
15:40  Tea  
16:10  Marco Cattaneo  A hierarchical model based on the likelihood function. If we interpret the statistical likelihood function as a measure of the relative plausibility of the probabilistic models considered, then we obtain a hierarchical description of uncertain knowledge, offering a unified approach to the combination of probabilistic and possibilistic uncertainty. The fundamental advantage of the resulting fuzzy probabilities with respect to imprecise probabilities is the ability of using all the information provided by the data. 
Tuesday: Regression Methods
Time  Speaker  Title 

9:15  Jochen Einbeck  Regression, robustness, imprecision, and 'trust'. 
10:00  Coffee break  
10:15  Gero Walter  Linear regression analysis under sets of conjugate priors 
11:00  Mike Lonergan  Are harbour seal populations declining? The problem of detecting changes in complex systems from small numbers of noisy samples. 
11:20  Discussions  
12:00  Lunch  
14:00  Thomas Augustin  Imprecision and random effects 
Robert Hable  Robust regression  
Carolin Strobl  Regression and classification 
Wednesday: Markov Theory
Time  Speaker  Title 

10:00  Damjan Skulj  Computational problems in the theory of
Markov chains with interval probabilities.
A Markov chain model is presented where precise probabilities are replaced with interval probabilities. The generalisation allows modelling situations where transition probabilities are allowed to vary within given intervals. Consequently, the distributions corresponding to further stages and limiting distributions are also sought in terms of interval probabilities. The calculations of the intervals corresponding to the steps of generalised Markov chains are computationally very complex, and therefore more efficient methods should be sought. A class of so called regular Markov chains with interval probabilities behaves in a similar ways as classical regular Markov chains. Another open problem is how to efficiently characterise regularity in terms of interval probabilities. 
11:00  Break  
11:15  Gert De Cooman  Imprecise Markov chains and their limit behaviour.
When the parameters of a finite Markov chain in discrete time, i.e., its initial and transition probabilities, are not well known, we can and should perform a sensitivity analysis. This is done by considering as basic uncertainty models the socalled credal sets that these probabilities are known or believed to belong to, and by allowing the probabilities to vary over such sets. This leads to the definition of an imprecise Markov chain. I will show that the time evolution of such a system can be studied very efficiently using socalled lower and upper expectations, which are equivalent mathematical representations of credal sets. I will also indicate how the inferred credal set about the state at time n evolves as n goes to infinity, and show that under quite unrestrictive conditions, this credal set converges to a uniquely invariant credal set, regardless of the credal set given for the initial state of the system. This effectively leads to a PerronFrobenius Theorem for a special class of nonlinear dynamical systems in discrete time. 
12:30  Lunch  
14:00  Richard Crossman  LongTerm Behaviour of Imprecise Markov Chains
In recent years work has begun upon considering the longterm behaviour of Markov Chains for which the elements of the transition matrix at a given time step n are not precisely known, nor assumed to be independent of time, but are known to exist within given bounds. However, in situations where the chain is known to contain an absorbing state (that is a state for which the lower probability of leaving the state is equal to 1), we can show that the longterm behaviour is often just what we would expect, i.e. certain absorption. In this talk, then, we consider how to condition upon nonabsorption for the case of imprecise Markov chains. 
15:00  Break  
15:15  Filip Hermans 
Thursday: Decision Making
Time  Speaker  Title 

9:30  Robert Hable  An introduction to decision making with imprecise probabilities. 
10:10  Thomas Augustin  Computational Aspects of Decision Making 
10:30  Coffee  
11:00  Marco Cattaneo  Statistical Decisions Based Directly on the Likelihood Function 
11:30  Malcolm Farrow and Michael Goldstein  AlmostPareto decision sets in imprecise utility hierarchies.
We develop methods for analysing decision problems based on multiattribute utility hierarchies, structured by mutual utility independence, in which tradeoffs between the various attributes are not precisely specified. Instead, our analysis is based on whatever limited collection of preferences we may assert between attribute collections. These preferences identify a class of Pareto optimal decisions. We show how to reduce the class further by combining rules which are almost equivalent and introduce general principles appropriate to selecting decisions in an imprecise hierarchy. The approach is illustrated by the design of a university course module. 
12:30  Lunch  
14:00  Matthias Troffaes and Nathan Huntley  Some issues in sequential decision making.
In this talk we will present a method for solving decision trees under Walley's maximality criterion. We discuss how maximality potentially leads to counterfactual decision sets, because a decision that is optimal in a subtree can be potentially absent in any optimal policy in the full tree. 
14:30  Thomas Augustin  A note on updating in decision theory. 
15:00  Break  
15:30  Peter Matthews  A Prototype Implementation of Bayesian Belief Networks for Engineering Design
Decision Support.
Engineering Design is a complex process wherein the fluidity of the domain during the earliest phases of the process resists deterministic models. To overcome this, a Bayesian Belief Network was induced for a given design domain, thereby providing a more fluid and dynamic stochastic domain representation. A prototype user interface for this BBN was developed using Visual Basic in Microsoft Excell, and this was subsequently tested with two different user groups and two design domains: (1) a set of student designers considering a conceptual car domain and (2) a team of industrial designers considering a gas turbine combustor. The key challenge identified during these trials was the understanding of the domain through a BBN and presentation of the BBN user interface. 
Friday: Principles and Methods of Statistics
Time  Speaker  Title 

9:30  Frank Coolen and Marco Cattaneo  Updating from setvalued observations 
10:30  Coffee  
10:45  Gero Walter  Handling priordata conflict in generalized Bayesian updating 
11:20  Frank Coolen and Thomas Augustin  Generalized Bayes rule and beyond 
12:30  Lunch  
14:00  Matthias Troffaes and Gero Walter  Software and simulation with imprecise probabilities 
15:00  Everyone  Looking back and future plans 
16:00  Everyone  Having a drink in town 
Confirmed Participants
 Thomas Augustin (Munich)
 Marco Cattaneo (Munich)
 Frank Coolen (Durham)
 Gert de Cooman (Gent)
 Jochen Einbeck (Durham)
 Malcolm Farrow (Newcastle)
 Mike Lonergan (St Andrews)
 Peter Matthews (Durham)
 Glenn Shafer (Rutgers School of Business, Newark)
 Damjan Skulj (Ljubljana)
 Matthias Troffaes (Durham)
 Ian Vernon (Durham)
 Rebecca Baker (Durham)
 Richard Crossman (Durham)
 Sebastien Destercke (IRSN)
 Mohamed Elsaeiti (Durham)
 Robert Hable (Munich)
 Filip Hermans (Gent)
 Zakia Kelantan (Durham)
 Christoph Knappik (Munich)
 Diana Maling (Durham)
 Tahani Maturi (Durham)
 Vicky Montgomery (Durham)
 Nathan Huntley (Durham)
 Carolin Strobl (Munich)
 Gero Walter (Munich)