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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Statistics Seminars: Multivariate modelling and inference under severe uncertainty and weak dependency assumptions.

Presented by Matthias Troffaes, Dept. Mathematical Sciences, Durham University

7 March 2011 15:15 in CM221

[joint research with Sebastien Destercke]

A pair of lower and upper cumulative distribution functions, also
called probability box or p-box, is among the most popular models used
to model severe uncertainty, when probabilities cannot be uniquely
identified. They arise naturally in expert elicitation, for instance
in cases where bounds are specified on the quantiles of a random
variable, or when quantiles are specified only at a finite number of
points. Many practical and formal results
concerning p-boxes already exist in the literature.

In this talk, I will discuss new efficient tools to construct
multivariate p-boxes and algorithms to draw inferences from them. For
this purpose, we formalise and extend the theory of p-boxes using
Walley's behavioural theory of imprecise probabilities, and heavily
rely on its notion of natural extension and existing results about
independence modeling. In particular, we allow p-boxes to be defined
on arbitrary totally preordered spaces, hence thereby also admitting
multivariate p-boxes via probability bounds over any collection of
nested sets. We focus on the cases of independence (using the
factorization property), and of unknown dependence (using the Frechet
bounds), and we show that our approach extends the probabilistic
arithmetic of Williamson and Downs. If time permits, two design
problems---a damped oscillator, and a river dike---will demonstrate
the practical feasibility of these new results.

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