John Fox (Oxford & UCL/Royal Free Hospital)
Arguing logically about risks: strengths, limitations and a request for assistance
Abstract: The standard mathematical treatment of risk combines numerical measures of uncertainty (usually probabilistic) and loss (money and other natural estimators of utility). There are significant practical and theoretical problems with this interpretation. A particular concern is that the estimation of quantitative parameters is frequently problematic, particularly when dealing with one-off events such as political, economic or environmental disasters.
Consequently practical decision-making under risk often requires extensions to the standard treatment.
An intuitive approach to reasoning under uncertainty has recently become established in computer science and cognitive science based on argumentation theory. On this approach theories about an application domain (formalised in a non-classical first-order logic) are applied to propositional facts about specific situations, and arguments are constructed for and/or against claims about what might happen in those situations. Arguments can also attack or support other arguments. Collections of arguments can be aggregated to characterize the type or degree of risk, based on the grounds of the arguments. The grounds and form of an argument can also be used to explain the supporting evidence for competing claims and assess their relative credibility. This approach has led to a novel framework for developing versatile risk management systems and has been validated in a number of domains, including clinical medicine and toxicology (e.g. www.infermed.com; www.lhasa.com). Argumentation frameworks are also being used to support open discussion and debates about important issues (e.g. see debate on "planet under pressure" at http://debategraph.org/Stream.aspx?nid=145319&vt=bubble&dc=focus).

Despite the practical success of argumentation methods in risk management and other kinds of decision making the main theories ignore quantitative measurement of uncertainty, or they combine qualitative reasoning with quantitative uncertainty in ad hoc ways. After a brief introduction to argumentation theory I will demonstrate some medical applications and invite suggestions for ways of incorporating uncertainty probabilistically that are mathematically satisfactory.

Chenlei Leng (Warwick)

High dimensional influence measure

Influence diagnosis is important since presence of influential observations could lead to distorted analysis and misleading interpretations. For high-dimensional data, it is particularly so, as the increased dimensionality and complexity may amplify both the chance of an observation being influential, and its potential impact on the analysis. In this article, we propose a novel high-dimensional influence measure for regressions with the number of predictors far exceeding the sample size. Our proposal can be viewed as a high-dimensional counterpart to the classical Cook's distance. However, whereas the Cook's distance quantifies the individual observation's influence on the least squares regression coefficient estimate, our new diagnosis measure captures the influence on the marginal correlations, which in turn exerts serious influence on downstream analysis including coefficient estimation, variable selection and screening. Moreover, we establish the asymptotic distribution of the proposed influence measure by letting the predictor dimension go to infinity. Availability of this asymptotic distribution leads to a principled rule to determine the critical value for influential observation detection. Both simulations and real data analysis demonstrate usefulness of the new influence diagnosis measure. This is joint work with Junlong Zhao, Lexin Li, and Hansheng Wang.

A copy of the paper is downloadable from http://arxiv.org/abs/1311.6636.