Bayesian Information Criteria and Problems of Parameter Identifiability

贝叶斯信息准则和参数可辨识性问题

• 批准号: 1305154
• 负责人: Mathias Drton
• 金额: $ 24万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-07-01 至 2016-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1305154&HistoricalAwards=false
• 关键词: Bayesian; Information; Criteria; Problems; Parameter

This project is concerned with statistical model selection by means of optimization of information criteria. Specifically, the investigator develops a generalization of the Bayesian information criterion for irregular model selection problems, such as determining the number of components in mixture models or the number of factors in latent factor models. The main difficulty in these irregular model selection problems is a lack of parameter identifiability. The investigator studies identifiability properties of widely used statistical models to provide the mathematical foundation for application of the new information criterion.Virtually every scientific data analysis brings about a problem of statistical model choice, where the different statistical models capture different scientific hypotheses. In many applications, the hypotheses involve latent variables that cannot or were not observed. Such latent variables could be, for instance, notions of intelligence in a psychological study or variables describing a patient's genetic composition in a medical study. Statistical models that are formulated using such latent variables typically lack the regularity properties that underlie the justification of standard statistical procedures. This project develops new statistical techniques for model selection that are theoretically justified and allow for an improved assessment of model uncertainty in a wide array of applications in which influential unobserved variables are at play.

该项目涉及通过优化信息标准来选择统计模型。具体地说，研究人员发展了非规则模型选择问题的贝叶斯信息准则的推广，例如确定混合模型中的组件数量或潜在因素模型中的因素数量。在这些不规则的模型选择问题中，主要的困难是缺乏参数可辨识性。研究人员研究了广泛使用的统计模型的可辨识性，为新的信息标准的应用提供了数学基础，实际上，每一次科学数据分析都会带来统计模型选择的问题，其中不同的统计模型捕获了不同的科学假设。在许多应用中，假设涉及不能观察到或没有观察到的潜在变量。例如，这些潜在变量可以是心理学研究中的智力概念，也可以是医学研究中描述患者基因组成的变量。使用这种潜在变量建立的统计模型通常缺乏作为标准统计程序理由的规律性属性。该项目为模型选择开发了新的统计技术，这些技术在理论上是合理的，并允许改进在各种应用中对模型不确定性的评估，在这些应用中，有影响的未观测变量在发挥作用。