Bayesian inference and relative belief, theory and applications

这项研究致力于开发先验的启发方法，测量先验引起的偏差，模型检验，先验数据冲突的检验，以及基于被称为相对信任度的证据的统计推理方法。 虽然统计方法在科学、技术和社会应用中正变得越来越重要，但对于什么构成统计问题的正确表述，从业人员之间几乎没有达成一致意见，而且，即使在就构成要素达成一致的情况下，对解决办法也可能存在分歧。诸如最近对p值使用的担忧之类的争议为这一点提供了一些证据。鉴于统计学家的作用是就如何在数据差异导致不确定性的情况下进行推理提供指导，该学科有必要尽可能多地解决这种冲突引起的模棱两可的问题。 分歧的中心点之一集中在先验概率分布的使用上，因为这些分布代表了对统计分析的明确的主观投入。这些投入似乎与调查员客观性的科学传统背道而驰。这种担忧无疑是有道理的，但它同时也忽略了一个明显的事实，即科学调查总是涉及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。这将在一定程度上通过为各种不同的背景制定启发式论点来实现，从而使选择以明确阐述的标准为基础。此外，将制定方法，以便对这些选择引起的偏差进行衡量和控制，并评估所作的选择是否与客观数据相冲突。 一旦选定了统计分析的成分，并至少如所述部分验证了这些成分，下一步就是将统计推断理论的规则与数据一起应用于这些成分，以得出推断。相关的推论理论应建立在如何衡量与感兴趣的问题有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，缺乏对这种证据衡量标准的明确定义，会产生另一种模棱两可的情况。相对信念推理理论的发展是为了提供一种基于统计证据的有效衡量标准的方法。这项研究建议还涉及进一步发展相关理论，并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用于近似的计算工具。

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.