"Bayesian inference, model checking, prior-data conflict, and inferences via Bayes factors and relative belief ratios"

这项研究致力于发展模型检验的统计方法、检验先验数据冲突、先验选择和统计推断的不变方法。应用于统计遗传学、市场营销学、机器学习和人口健康研究中的实际问题。 统计分析取决于分析员所做的选择。这些选择包括描述观测数据生成的抽样模型，以及描述抽样模型内真实分布的不确定性的先验的选择。在这两种情况下，这些选择都是主观做出的。虽然这样的选择应该基于个人的最佳判断，但一个基本原则是，这些选择应该与客观数据进行比较，以确保它们是有意义的。模型检查是一种常见的统计活动，但检查先验数据冲突并不常见。造成这种情况的至少部分原因是，当这种冲突存在时，人们不清楚该怎么做。这项研究涉及如何为特定类型的问题选择先验，如Logistic回归和结构方程建模，如何评估是否有先验数据 冲突存在，以及当冲突发生时该如何处理。 另一个基本原则与不变性有关。当分析师做出无法对照数据进行检查的选择时，要求分析在所做选择下保持不变是很自然的。数据的特定表示法的选择和统计模型的参数化就是这种选择的例子。这项研究的另一个方面是发展贝叶斯方法的理论和实践实现方面，该方法在这样的选择下是不变的，用于模型检验、检验先验以及基于给定模型和先验的推理。

This research is concerned with developing statistical methodology for model checking, checking for prior-data conflict, selection of priors and invariant methods for statistical inference. Applications are made to practical problems in statistical genetics, marketing, machine learning and population health studies. Statistical analyses are dependent upon choices made by an analyst. These choices include the sampling model to describe the generation of observed data and the choice of a prior that describes uncertainties about the true distribution within the sampling model. In both cases these choices are made subjectively. While such choices should be made based upon one's best judgement, a basic principle is that such choices should be checked against the objective data to ensure that they make sense. Model checking is a common statistical activity but checking for prior-data conflict is not. At least part of the reason for this is the ambiguity about what to do when such a conflict exists. This research is concerned with how to select priors for particular classes of problems, such as logistic regression and structural equation modelling, how to assess whether or not prior-data conflict exists and what to do when this occurs. Another basic principle concerns invariance. When an analyst makes a choice that cannot be checked against the data, then it is natural to require that the analysis be invariant under the choice made. The choice of a particular representation of the data and the parameterization of a statistical model are examples of such choices. Another aspect of this research is concerned with developing the theoretical and practical implementational aspects of Bayesian methodology that is invariant under such choices for model checking, checking the prior and for inference based on a given model and prior.