Mathematical Sciences: Strategies for Bayesian Data Analysiswith Application to Quantal Bioassay and Geographic Disease Occurrence Models

最近，蒙特卡罗方法在从高维非归一化节理密度中获取样本方面取得了重大进展。事实证明，这些技术在拟合结构化随机效果模型方面特别有价值。在这种情况下，后验分布的分析检查是不可行的，但抽样可以任意准确地估计后验分布的任何特征，并有望拟合以前无法获得的巨大范围的模型。现在，必须将注意力转向贝叶斯数据分析工具的开发。与模型开发艺术的非正式性一致，我们建议开发具有EDA风格的非正式工具，以自然地与用于拟合模型的基于抽样的方法相匹配。应用将在两个生物识别领域，量子生物测定和地理疾病地图。当代的统计工作是由严肃的应用推动的。在这样的应用中，现实的模型必然是复杂的，其中包含许多未知因素。事实上，可能有几个收集了数据的合理模型，问题是如何将这些模型与我们可能会问的几个模型选择相匹配，这些模型中是否有一个是好的，以及我们更喜欢哪一个。数据分析师的角色是为这些问题提供答案。拟议的研究旨在通过提供进行拟合的统一战略和研究模型的充分性和选择的一套相关工具来帮助数据分析员整个方法的核心是最基本的统计思想--抽取样本以了解模型未知数。我们建议将这种方法应用于两个生物识别领域。其中一个考虑了疾病发生的地理模式。另一种涉及由于暴露于毒素的变化而对种群的毒性变化。

Recently there have been major advances in the development of monte carlo strategies to obtain samples from high dimensional nonnormalized joint densities. These techniques have proved especially valuable in fitting structured random effects models. In such settings, Analytic examination of the posterior distribution is infeasible but sampling enables arbitrarily accurate estimation of any features of the posterior with the promise of fitting an enormous range of previously inaccessible models attention must now turn to the development of tools for bayesian data analysis. Consistent with the informality of the art of model development we propose to develop informal tools with an eda flavor to mesh naturally with the sampling based approaches used to fit the model. Application will be in two Biometric areas, quantal bioassay and geographic disease mapping. CONTEMPORARY STATISTICAL WORK IS DRIVEN BY SERIOUS Applications. Realistic Models in such applications will necessarily be complex incorporating many unknowns. Indeed, there may be several plausible models with collected data, the question arises of how to fit such models with several choices of models we might ask if any of them are good and which one we prefer. The role of the data analyst is to provide answers to these questions. The proposed research is intended to help the data analyst by providing a unifying strategy for carrying out the fitting and an associated set of tools for studying adequacy of and choice of models at the heart of the entire approach is the most elementary of statistical ideas - drawing samples to learn about model unknowns. We propose to utilize this approach in two biometric areas of application. One considers geographic patterns of disease occurrence. The other involves the change in toxicity to a population due to change in exposure to a toxin.