评论：分层模型第二层的贝叶斯检验

Checking for prior-data conflict using prior to posterior divergences

When using complex Bayesian models to combine information, the checking for consistency of the information being combined is good statistical practice. Here a new method is developed for detecting prior-data conflicts in Bayesian models based on comparing the observed value of a prior to posterior divergence to its distribution under the prior predictive distribution for the data. The divergence measure used in our model check is a measure of how much beliefs have changed from prior to posterior, and can be thought of as a measure of the overall size of a relative belief function. It is shown …

关于J.N.“频率论和贝叶斯方法对调查抽样实践的影响：选择性评估”的讨论。K.饶

Discussion of "Impact of Frequentist and Bayesian Methods on Survey Sampling Practice: A Selective Appraisal" by J. N. K. Rao

这一评论强调了模型检验和模型拟合的重要性时，有限的人口数量的推断。它还表明了在对小型亚群进行推断时使用单位水平模型的价值，即“小区域”分析[arXiv：1108.2356]。

Using prior expansions for prior-data conflict checking

Any Bayesian analysis involves combining information represented through different model components, and when different sources of information are in conflict it is important to detect this. Here we consider checking for prior-data conflict in Bayesian models by expanding the prior used for the analysis into a larger family of priors, and considering a marginal likelihood score statistic for the expansion parameter. Consideration of different expansions can be informative about the nature of any conflict, and extensions to hierarchically specified priors and connections with other approaches t…

近似后验重新校准

Approximate posterior recalibration

本文提出两种方法扩展基于模拟的校准检查以扩大后验不确定性区间，旨在实现边缘校准，并讨论后验校准在分层模型中的应用挑战。

A Hierarchical Framework for Correcting Under-Reporting in Count Data

Tuberculosis poses a global health risk and Brazil is among the top twenty countries by absolute mortality. However, this epidemiological burden is masked by under-reporting, which impairs planning for effective intervention. We present a comprehensive investigation and application of a Bayesian hierarchical approach to modelling and correcting under-reporting in tuberculosis counts, a general problem arising in observational count data. The framework is applicable to fully under-reported data, relying only on an informative prior distribution for the mean reporting rate to supplement the part…

贝叶斯符合性评估（交叉匹配）

Commentary on Bayesian coincidence assessment (cross-matching)

本文是对Tamas Budavari的演讲“关于天文学中的统计交叉识别”的特邀评论，该演讲于2011年6月在宾夕法尼亚州立大学举行的现代天文学V会议的统计挑战。我首先简要回顾了以前在天文学中对方向和时空巧合进行概率（贝叶斯）评估的工作（例如，跨多个目录的对象的交叉匹配或交叉识别）。然后，我讨论了一个开放的问题，在最近的创新工作Budavari和他的同事在大规模概率交叉识别：如何分配先验概率，在分析中发挥重要作用。一个简单的玩具问题，我展示了贝叶斯多层次建模（分层贝叶斯）提供了一个原则性的框架，证明和推广实用的经验法则，已成功地使用Budavari的团队分配先验。

使用分裂预测检验的校准模型批评

Calibrated Model Criticism Using Split Predictive Checks

针对现有贝叶斯模型检验方法在校准性、自动化与效率间的权衡问题，提出结合后验预测检验优势与良好校准性的分裂预测检验，构建两类方法的渐近理论并通过模拟和真实数据验证其效用与优势。

Multivariate Hierarchical Frameworks for Modelling Delayed Reporting in Count Data

In many fields and applications count data can be subject to delayed reporting. This is where the total count, such as the number of disease cases contracted in a given week, may not be immediately available, instead arriving in parts over time. For short term decision making, the statistical challenge lies in predicting the total count based on any observed partial counts, along with a robust quantification of uncertainty. In this article we discuss previous approaches to modelling delayed reporting and present a multivariate hierarchical framework where the count generating process and delay…