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

在刑事诉讼、公共卫生干预和制定新立法等情况下，往往雇用统计学家将问题的口头描述转化为统计模型。这些模型不仅可以被决策者用来为他们决定推进的判断提供信息，而且还允许专家将他们对问题的理解形式化，并将他们拥有的特定知识集成到模型中。图形模型是生成统计模型的特别有吸引力的工具，因为它们为专家提供了对底层统计关系的结构性和可视化理解。由于模型的可解释性，这些模型可以被统计学家、领域专家和不太专业的用户使用。这种可解释的模型在人工智能时代尤其具有吸引力，因为统计模型的透明度、可审计性和可解释性对于使用统计模型的信心非常重要。链式事件图是该领域的一个重要创新。首先是为了克服使用贝叶斯网络建模的局限性而开发的，它们起源于事件树结构。事件树对数据集中的不同特征进行分区，以便特征和结果的每个唯一组合遵循唯一的路径。与贝叶斯网络不同，通过删除事件树中的边，ceg允许在模型中直接表示不对称。给定一个事件树，专家通过简单地给顶点上色来表达可交换性判断，这样任何相同颜色的节点都有相同的发生概率（相同的阶段）。通过合并颜色和结构相同的顶点，生成的阶段树被转换为链式事件图。分支末端的所有顶点都被压缩成一个顶点，称为汇聚点。然后获得每个阶段的狄利克雷先验，并可以通过图结构用数据更新，形成可分析的可处理后验。对链式事件图进行了一些扩展，以考虑使用各种数据流进行前后分析的时间适应性。这些变种，被称为动态链事件图（DCEGs），包括离散时间步的一步预测（Freeman, 2010），将无限事件树表示为与半马尔可夫模型（Barclay等人，2015）相连接的CEGs，以及连续时间DCEGs (CT-DCEGs)，其模拟CEG内不同状态下的非指数分布保持时间（Shenvi & Smith, 2020）。在这些扩展的基础上，我希望通过空间进一步扩展DCEG模型。DCEGs还没有被用于比较不同地理区域的情况——这种扩展将允许通过单一层次结构对具有不同地理区域的不同阶段树的单一过程的CEG模型进行建模。虽然我最初的研究将集中在使用CEG来模拟犯罪数据，但目标是开发具有广泛适用性的时空CEG技术。ceg使用直观和可解释的结构，从广泛的专家中引出丰富而复杂的统计模型。为了将专家在ceg方面的直觉和信心带到更广泛的重要问题上，需要进一步的研究将它们发展成与参数时空模型竞争的模型。

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.