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

最近，在开发方面取得了重大进展， 从高维数据中获取样本的蒙特卡洛策略 非标准化联合密度。 这些技术已经证明 在拟合结构化随机效应模型时尤其有价值。 在这种情况下，分析检查后， 分布是不可行的，但抽样允许任意 准确估计后验的任何特征， 承诺适应以前无法达到的巨大范围 模型的注意力现在必须转向工具的开发， 有效数据分析 符合非正式的 模型开发的艺术，我们建议开发非正式工具 具有EDA风味，以自然地与基于 用于拟合模型的方法。 应用程序将在两个 生物测定区、量子生物测定与地理疾病绘图。 认真做好当代统计工作 应用. 这些应用中的真实模型将 必然是复杂的，包含许多未知数。 的确， 可能有几个合理的模型与收集的数据， 问题是如何使这些模型适合几种选择 我们可能会问他们中的任何一个是好的，哪一个我们 喜欢. 数据分析师的角色是提供以下问题的答案 这些问题。 拟议的研究旨在帮助 数据分析师通过提供一个统一的战略， 拟合和一套相关的工具， 整个方法的核心是 最基本的统计思想-抽取样本， 了解未知模型。 我们建议采用这种方法 在两个生物识别领域的应用。 一是考虑地理 疾病发生的模式。 另一个涉及到 由于暴露于毒素的变化而对人群产生的毒性。

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.