Rejoinder: Bayesian Checking of the Second Levels of Hierarchical Models

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 …

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…

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…

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。

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。

Bayesian clustering using random effects models and predictive projections

Linear mixed models are widely used for analyzing hierarchically structured data involving missingness and unbalanced study designs. We consider a Bayesian clustering method that combines linear mixed models and predictive projections. For each observation, we consider a predictive replicate in which only a subset of the random effects is shared between the observation and its replicate, with the remainder being integrated out using the conditional prior. Predictive projections are then defined in which the number of distinct values taken by the shared random effects is finite, in order to obt…

异方差健康结局数据的贝叶斯核机器回归

Bayesian kernel machine regression for heteroscedastic health outcome data

本文针对环境流行病学中BKMR模型误差项恒定方差假设不成立的问题，开发了异方差HBKMR方法，通过贝叶斯分层方差模型更新健康效应估计，并在两项真实金属暴露案例中显著提升了模型拟合度。

Bayesian modelling of lung function data from multiple-breath washout tests

Paediatric respiratory researchers have widely adopted the multiple-breath washout (MBW) test because it allows assessment of lung function in unsedated infants and is well suited to longitudinal studies of lung development and disease. However, a substantial proportion of MBW tests in infants fail current acceptability criteria. We hypothesised that a model-based approach to analysing the data, in place of traditional simple empirical summaries, would enable more efficient use of these tests. We therefore developed a novel statistical model for infant MBW data and applied it to 1,197 tests fr…