Spatio-temporal Chain Event Graphs for translating expert judgement into complex statistical models. (Ref:4659)

In situations such as criminal proceedings, public health intervention and creating new legislation, statisticians are often employed to transform verbal descriptions of problems into statistical models. Not only can these models be used by decision makers to inform the judgements they decide to push forwards, but they also allow experts to formalise their understanding of a problem and integrate particular knowledge they have into a model. Graphical models are particularly attractive tools for generating statistical models as they offer the expert a structural and visual understanding of the underlying statistical relationships. Once constructed, these models can be used by statisticians, domain experts and less expert users alike, owing to their interpretability. Such interpretable models are particularly attractive in the age of AI, where transparency, auditability and interpretability of statistical models is so important for confidence in their use.

Chain Event Graphs are an important innovation in this area. First developed to overcome the limitations of modelling using Bayesian Networks, they arise from an event tree structure. Event trees partition the different features in a data set so that every unique combination of features and outcomes follows a unique path. CEGs allow representation of asymmetry directly within the model, unlike Bayesian Networks, by deleting the edges within the event tree. Given an event tree, experts express exchangeability judgements by simply colouring vertices, so that any nodes of the same colour are given the same probability of occurrence (the same stage). The resulting staged tree is converted to a Chain Event Graph by merging the vertices whose colours and structure are the same. All vertices at the end of a branch are contracted into a single vertex, known as the sink. Dirichlet priors on each stage are then obtained and can be updated with data through the graph structure to form an analytically tractable posterior.

Several extensions have been made to Chain Event Graphs to consider adaptions through time using various streams of data to perform prior to posterior analyses. These variants, known as Dynamic Chain Event Graphs (DCEGs) include one-step predictions with discrete time-steps (Freeman, 2010), representing infinite event trees as CEGs with links to semi-Markov models (Barclay, et al., 2015), and continuous time DCEGs (CT-DCEGs) which model non-exponentially distributed holding times at various states within the CEG (Shenvi & Smith, 2020). Building on these extensions, I wish to further extend the DCEG model through space. DCEGs have not yet been used to compare situations in different geographical areas - this extension would allow a CEG model of a single process with different staged trees for different geographical areas to be modelled through a single hierarchical structure. Though my initial research will focus on using CEGs to model crime data, the aim is to develop spatio-temporal CEG technologies with wide applicability. CEGs use intuitive and explainable structures to elicit rich and complex statistical models from a wide array of experts. Further research to develop them into competitors with parametric spatio-temporal models is needed in order to bring the intuition and confidence experts have in CEGs to a much wider class of important problems.