Bayesian methods and computation in complex models

复杂模型中的贝叶斯方法和计算

• 批准号: 402294-2011
• 负责人: Muthukumarana, PalavinnageSaman
• 金额: $ 1.24万
• 依托单位: University of Manitoba
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635894
• 关键词: Bayesian; methods; computation; complex; models

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.

拟议的研究计划的主要目标是开发新的贝叶斯方法，处理复杂的模型结构。两个主要的应用领域是网络数据和有序调查数据。对于大多数标准类型的数据，有成熟的方法指导抽样、建模和推断。然而，在许多应用领域，特别是网络问题和调查数据，收集了非标准的数据集，需要创新的分析。例如，数据可以是连续的或离散的，可能存在复杂的依赖关系，关系可以是有向的或无向的，数据可以是动态的，多变量的，具有缺失值，包括协变量等。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，复杂的后验通常会导致无法通过分析解决的集成问题。相反，模拟程序经常被用来从后验样本变量。在这一建议中，我考虑制定新的方法，以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，如引文分析，它确定了在一个研究领域有影响力的论文，流行病学中疾病传播的动态，确定最有效的领域，在商业和电信中的产品/服务分布和政治学中的联盟形成动态。在调查数据方面，作为本提案中所提议方法的副产品，可以确定相应绩效不佳或异常的调查问题，以及多余的调查问题。这在测量成本管理中具有重要意义。