Simon Shaw

My interests lie in Bayesian approaches to statistics, in particular Bayes linear methods, the analysis of collections of (second-order) exchangeable sequences, graphical models and uses of conditional independence.

I have recently been concerned with sampling multivariate vectors which may be judged to be either normally distributed or, more generally, second-order exchangeable. A typical simplifying assumption is that the vectors are drawn from an infinite population. I have been interested in understanding when a full accounting of the finiteness is significant, for example in determining whether or not the sampling fraction is ignorable. Extensions to the model I have explored include multivariate cluster sampling with exchangeable clusters and problems in which individuals belong to different groups where the underlying covariance matrices are separable between groups and variables. Real life applications include situations where one might want to sample a non-trivial proportion of economic units in a region to assess total economic activity in that region or in the modelling of a complex system, such as the climate, where at any given time there might be a number of different models of the system, for example from different research groups.

Another focus is in the creation of generalised Bayesian graphical models which combine both Bayes linear specifications and full probabilistic specifications, typically using the method of Bayes linear kinematics. There are many practical cases when it would be advantageous to utilise a graphical model which has different levels of detail in the stochastic description in different parts of the model, one example being that of software testing.

A final, slightly different, strand of my research is in areas of operational research, in particular the development and analysis of non-parametric predictive inference (NPI)-based strategies for age replacement of components.