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，统计学家经常被雇来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整合到一个模型中。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基本统计关系的结构和视觉理解。一旦构建了这些模型，由于其可解释性，统计学家、领域专家和不太专业的用户都可以使用它们。这种可解释模型在人工智能时代特别有吸引力，在这个时代，统计模型的透明度、可审核性和可解释性对于它们的使用信心是如此重要。链事件图是这一领域的重要创新。它们最初是为了克服使用贝叶斯网络建模的局限性而开发的，它们源于事件树结构。事件树划分了数据集中的不同特征，从而使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，CEGS通过删除事件树中的边，允许直接在模型中表示不对称性。在给定事件树的情况下，专家通过简单地给顶点着色来表示可互换性判断，以便相同颜色的任何节点被赋予相同的发生概率(相同的阶段)。通过合并颜色和结构相同的顶点，将得到的分级树转换为链事件图。分支末端的所有顶点都收缩为单个顶点，称为汇点。然后获得每个阶段的Dirichlet先验，并可以通过图结构用数据来更新这些先验，以形成分析上可处理的后验。已经对事件图进行了几个扩展，以使用在后验分析之前执行的各种数据流来考虑随时间变化的适应性。这些变体被称为动态链事件图(DCEG)，包括带有离散时间步长的一步预测(Freeman，2010)，将无限事件树表示为链接到半马尔可夫模型的CEG(Barclay，等人，2015)，以及连续时间DCEG(CT-DCEG)，其模拟CEG内不同状态下的非指数分布的持有时间(Shenvi&Smith，2020)。在这些扩展的基础上，我希望在太空中进一步扩展DCEG模式。DCEG尚未用于比较不同地理区域的情况--这一扩展将使具有不同地理区域的不同分级树的单一进程的CEG模型能够通过单一的等级结构进行建模。虽然我最初的研究重点是使用CEGS对犯罪数据进行建模，但目的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，从广泛的专家那里得出丰富而复杂的统计模型。需要进一步的研究，将它们发展成具有参数时空模型的竞争者，以便将专家们对CEGS的直觉和信心带到更广泛的重要问题类别中。

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.