5.00pm – 5.40pm: Lorna Barclay (University of Warwick)

An Introduction to Chain Event Graphs

The Chain Event Graph (CEG) is proving to be a useful framework for modelling discrete processes which exhibit strong asymmetric dependence structures between the variables of the problem. It is a class of graphical models which generalises the discrete Bayesian Network and which is derived from a probability tree by merging the vertices whose associated conditional probability distributions are the same.

In this talk I will give an introduction to Chain Event Graphs and demonstrate how the CEG can provide substantial improvements to the usual Bayesian Network by applying it to a birth cohort study on children’s health. I will further discuss the advantage of employing CEGs to represent studies where missingness is influential and data cannot plausibly be hypothesised to be missing at random. Consequently, I will show how the CEG can be used to define categories of variables which are informative for a later analysis. This will be illustrated through a large Cerebral Palsy cohort study.

5.40pm – 6.40pm: Peter Thwaites (University of Leeds)

The use of Chain Event Graphs in Decision Analysis & Game Theory

The chain event graph (CEG) was originally developed as an alternative probabilistic graphical model for the representation & analysis of asymmetric processes. That the CEG could also be used for modelling asymmetric decision problems came as a welcome bonus. This talk concentrates on this aspect of CEG analysis, and on how they might be used in Game Theory.

If the influence diagram (ID) depicting a Bayesian game is common knowledge to its players then additional assumptions may allow the players to make use of its embodied irrelevance statements. They can then use these to discover a simpler game which still embodies both their optimal decision policies. However the impact of this result has been rather limited because many common Bayesian games do not exhibit sufficient symmetry to be fully and efficiently represented by an ID.

If a CEG is used to depict such a game, then the full conditional independence structure of the game can be read from the graph, which makes it possible for rational players to make analogous deductions, assuming the topology of the CEG as common knowledge. These new techniques are illustrated through an example modelling risks to electronic communication.

François Caron (Oxford)
Bayesian nonparametric models for bipartite graphs

In this talk I will present a novel Bayesian nonparametric model for bipartite graphs, based on the theory of completely random measures. The model is able to handle a potentially infinite number of nodes and has appealing properties; in particular, it may exhibit a power-law behavior for some values of the parameters. I derive a posterior characterization, a generative process for network growth, and a simple Gibbs sampler for posterior simulation. Finally, the model is shown to provide a good fit to several large real-world bipartite social networks.

Davide Pigoli (Warwick)
Statistical methods for phonetic covariance operators in comparative linguistics

Comparative linguistics is concerned with the exploration of languages evolution. The traditional way of exploring relationships across languages consists of examining textual similarity. However, this neglects the phonetic characteristics of the languages. Here a novel approach is proposed to incorporate phonetic information, based on the comparison of frequency covariance structures in spoken languages. In particular, the aim is to explore the relationships among Romance languages and how they have developed from their common Latin root. The covariance operator being the statistical unit, a framework is illustrated for inference concerning the covariance operator of a functional random process. First, the problem of the definition of possible metrics for covariance operators is considered. In particular, an infinite dimensional analogue of the Procrustes reflection size and shape distance is developed. Then, distance-based inferential procedures are proposed for estimation and hypothesis testing. Finally, it is shown that the analysis of pairwise distances between phonetic covariance structures can provide insight into the relationships among Romance languages. Some languages also present features that are not completely expected from linguistics theory, indicatingnew directions for investigations.