Dependence Elicitation for Risk and Decision Analysis


A Public Lecture by Professor Tim Bedford

(Slides can be found here.)

Thursday, October 12th 2017 at 16.15-17.00
Hall M1Otakaari 1, Aalto University School of Science
Otakaari 1, Espoo.

Abstract (by Tim Bedford, Christoph Werner and John Quigley)

When assessing uncertainty, whether for risk assessment or as part of a decision analysis, it is important to consider whether the uncertainty we wish to model for variables of interest should include stochastic dependency. Simple examples suffice to show the real significance of capturing dependency in the outputs of models. Such dependency often arises because there are factors outside the scope of the model which link uncertainties between the variables within the model.

Copulas and vines provide mathematical structures, generalizing parametric multivariate distributions, with which dependency can – in principle – be modelled. However they do not address the issue of actually quantifying a dependence structure in a specific context. In practice this has often been done by asking experts to specify bivariate correlations – which makes the implicit assumption that correlation is a quantity that experts should be good at specifying.  A better, but less used approach is to ask about conditional exceedance probabilities for one variable, given an exceedance event for another: For example, the probability that X exceeds its median given that Y exceeds its median.

In this talk we shall discuss new approaches to dependence elicitation which generalise the exceedance approach. We show that multiple elicitations of exceedance probabilities can be made with exact lower and upper feasible bounds generated from previous elicitations by an LP problem. The elicitation process makes use of an approach to rationale development by the individual experts that both allows them to share understandings of the qualitative factors leading to dependence, and also allows them to provide insights to the owners and stakeholders of the broader risk management framework.  This feedback is considered a critical element of risk management and is incorporated explicitly into risk management standards. This work has benefited greatly from support of the COST network IS1304.

The Public Lecture is organized by the Systems Analysis Laboratory research group at the Department of Mathematics and Systems Analysis of Aalto University School of Science.


As an Associate Principal professor Bedford leads the Research and Innovation portfolio in the University Executive Team, working in close collaboration with the Principal and Deputy Associate Principals Professors Hamill, Kerr and McArthur.

Professor Bedford has two roles at the University: He leads the Research and Innovation portfolio within the university, with a particular focus on the Innovation aspects, working closely with other senior colleagues each of whom has specific responsibilities within R&I; He is also Professor of Decision and Risk Analysis within the Management Science Department of the Business School.

In his role as Professor of Decision and Risk Analysis, Professor Bedford continues to teach, supervise PhDs and conduct research in probabilistic risk analysis, uncertainty modelling, reliability and maintenance modelling, structured expert judgement and decision analysis.

Prof Bedford has been active in various professional societies, amongst others the European Safety and Reliability Association and the Dutch Reliability Society, of which he was Chair. He has been Chair of the Committee of Professors of Operational Research, the network of UK OR Professors and was a member of the Board of Directors of the European Safety Reliability and Data Association ESReDA. He has been elected a Fellow of the UK Safety and Reliability Society and of the Institute for Mathematics and its Applications. He was a member of the EPSRC Mathematics Programme Strategic Advisory Panel. He has carried out research and consultancy projects for a range of companies including Aveco, ESTEC, MoD, DSTL, Railway Safety, Magnox, Netherlands Ministry for Water Management, Philips, Scottish Power, SSE. He was awarded the Donald Julius Groen prize for 2009 by the IMechE Safety and Reliability Group, and in 2013 was awarded the Lloyds Risk Prize for work on Societal Risk. He was co-chair of the EURO2015 Conference - the major European conference on Operational Research in 2015, and also co-chair of the ESREL2016 Conference – the major European conference on Safety and Reliability.


The Public Lecture is open to all interested participants. If you plan to attend, we kindly request you to send an email to Juho Roponen (

After the lecture there will be an opportunity for informal discussions.

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