Bayesian methods and computation in complex models

提出的研究计划的主要目标是开发新的贝叶斯方法来处理复杂的模型结构。两个主要的应用领域是网络数据和顺序测量数据。对于大多数标准类型的数据，都有完善的方法来指导抽样、建模和推理。然而，在许多应用领域，特别是网络问题和调查数据，收集了需要创新分析的非标准数据集。例如，数据可能是连续的或离散的，可能存在复杂的依赖关系，关系可能是有向的或无向的，数据可能是动态的，多变量的，有缺失值，包括协变量等。在这些问题中，也有可能存在数据分区，使得类中的数据相似。这些类型的复杂性很少允许研究人员考虑一个简单的模型结构来解释问题的现实。在复杂模型的情况下，复杂后验通常会导致无法解析解决的集成问题。相反，模拟程序通常用于从后验中抽样变量。在本建议中，我考虑开发新的方法来促进网络和调查模型的抽样、建模和推理。这些方法将被推广到网络分析的许多应用中，例如引用分析，用于确定研究领域中有影响力的论文，流行病学中疾病传播的动态，确定商业和电信中产品/服务分布的最有效领域，以及政治学中联盟形成的动态。在调查数据的背景下，作为本建议中建议的方法的副产品，人们可以识别相应表现不佳或异常的调查问题，以及冗余的调查问题。这在测量成本管理中是很重要的。

The main objective of the proposed research program is to develop new Bayesian methodologies that deal with complex model structures. Two of the main areas of application are network data and ordinal survey data.For most standard types of data, there are well-developed approaches guiding sampling, modelling and inference. However, in many areas of application including, in particular, network problems and survey data, non-standard datasets have been collected that require innovative analyses. As an example, Data may be continuous or discrete, there may be complex dependencies, relationships may be directed or non-directed, data may be dynamic, multivariate, have missing values, include covariates, etc. In these problems, it is also possible that there are partitions of the data such that data within classes are similar. These types of complexities rarely allow a researcher to consider a simple model structure that explains the reality of the problem.In the case of complex models, complex posteriors are usually leading to integration problems that cannot be solved analytically. Instead, simulation procedures are often used to sample variates from the posterior. In this proposal, I consider the development of new methodologies to facilitate sampling, modelling and inference on network and survey models. The methodologies will be generalized to many applications of network analysis such as citation analysis which identifies influential papers in a research area, dynamics of the spread of disease in epidemiology, identifying most effective areas for product/service distributions in business and telecommunications and coalition formation dynamics in political science. In the context of survey data, as a by-product of the proposed methodologies in this proposal, one can identify survey questions where the corresponding performance has been poor or exceptional and also the survey questions that are redundant. This is important in the cost management of survey.