Bayesian inference and relative belief, theory and applications

贝叶斯推理和相对信念、理论和应用

• 批准号: RGPIN-2017-06758
• 负责人: Evans, Michael
• 金额: $ 2.19万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=709712
• 关键词: Bayesian; inference; relative; belief; theory

This research is concerned with developing methodology for the elicitation of priors, measuring the bias induced by a prior, model checking, checking for prior-data conflict and methods for statistical inference based upon a measure of evidence known as the relative belief ratio. While statistical methodology is becoming increasingly important in scientific, technological and social applications, there is little agreement among practitioners as to what constitutes the correct formulation of a statistical problem and furthermore, even when the ingredients are agreed upon, there may be disagreement concerning the solution. Controversies such as the recent concerns over the use of p-values provide some evidence for this. Given that the role of a statistician is to provide guidance on how one is to reason in contexts where data variation results in uncertainty, it is necessary for the discipline to do as much as possible to resolve the ambiguities arising from such conflicts. One of the central points of disagreement focuses on the use of prior probability distributions as these represent clear subjective inputs into statistical analyses. These inputs would seem to run contrary to the scientific tradition of the objectivity of the investigator. This concern is undoubtedly valid, but at the same it ignores the obvious fact that scientific investigations always involve subjective aspects resulting from the choices made by the scientist. The role of this research is to develop tools for dealing with this subjectivity in a scientifically valid fashion. This will be accomplished in part through the development of elicitation arguments for a broad variety of contexts so that the choices are based on clearly articulated criteria. Furthermore, methodology will be developed that allows for the measurement and control over the biases introduced by these choices and allows for the assessment of whether or not the choices made are in conflict with the objective data. Once the ingredients of a statistical analysis have been chosen, and at least partially validated as described, the next step is to apply the rules of a theory of statistical inference to these ingredients together with the data to derive inferences. A relevant theory of inference should be based on a clear definition of how to measure the statistical evidence relevant to questions of interest. For many approaches to statistical theory, the lack of a clear definition of such a measure of evidence produces yet another ambiguity. The theory of relative belief inference has been developed to provide an approach that is based on a valid measure of statistical evidence. This research proposal is also concerned with the further development of the associated theory and the application of this to a broad variety of statistical problems with practical relevance. This research will also require the development of suitable computational tools for approximations.

本研究关注的是开发方法的启发先验，测量的偏见引起的先验，模型检查，检查先验数据冲突和方法的统计推断的基础上的证据被称为相对置信比的措施。 虽然统计方法在科学、技术和社会应用中变得越来越重要，但从业者对于什么构成统计问题的正确表述却几乎没有达成一致，此外，即使就要素达成一致，也可能存在分歧关于解决方案。最近对p值使用的关注等争议为这一点提供了一些证据。鉴于统计学家的作用是指导如何在数据变化导致不确定性的情况下进行推理，该学科有必要尽可能解决这种冲突所产生的模糊性。 分歧的中心点之一集中在先验概率分布的使用，因为这些代表了统计分析的明显主观输入。这些投入似乎违背了调查人员客观性的科学传统。这种担心无疑是有道理的，但同时它也忽略了一个明显的事实，即科学研究总是涉及到科学家所作选择的主观方面。这项研究的作用是开发工具，以科学有效的方式处理这种主观性。 这将部分地通过为各种各样的背景发展启发论点来实现，以便选择基于明确阐述的标准。此外，还将制定方法，以衡量和控制这些选择所带来的偏差，并评估所作的选择是否与客观数据相冲突。 一旦选择了统计分析的成分，并且至少部分地如所描述的那样进行了验证，下一步就是将统计推断理论的规则应用于这些成分以及数据以得出推断。一个相关的推理理论应该建立在如何衡量与感兴趣的问题相关的统计证据的明确定义的基础上。对于统计理论的许多方法来说，缺乏对这种证据度量的明确定义会产生另一种模糊性。 相对信念推理的理论已经发展到提供一种基于统计证据的有效测量的方法。本研究建议还涉及相关理论的进一步发展，以及将其应用于各种具有实际意义的统计问题。 这项研究还需要开发适当的近似计算工具。