Mathematical Sciences: Problems in Hierarchical Model Determination

Gelfand 最近的计算技术进步使得拟合 分层模型在广泛的应用中。 与 这种能力引起了模型确定中的各种问题。 这 研究是在一组模型中选择最佳模型， 这样的模型。 它关注的是善与恶之间的权衡 适合和吝啬和不适当或缺点的 习惯标准。 该研究还涉及模型问题 适足性 对于分层模型，模型故障可能发生在每个 阶段 确定是否存在此类故障的方法， 由调查员审查其性质。 最后针对 层次模型超先验规范通常是模糊的。 这 工作考虑的条件下，所得的后验是一个 适当的分配。 统计学的现代智力贡献是建模和 推论 在与其他领域的科学家合作时， 统计学家帮助制定适当的模型， 科学家的问题和数据，以及表明如何推理， 它提供了问题的答案， 科学家的调查。 随着高可用性 随着计算速度的提高，越来越复杂的模型正在被 考虑允许研究工作集中在 确定最适合应用的模型 而不是勉强接受一个明显不合适的方案。 尽管如此，模型必须提供一些简化，否则它们就是 并不比它们是一种复杂的现象 建模 这项研究解决了几个重要问题， 确定满意模型的过程。

Gelfand Recent computational advances have made it feasible to fit hierarchical models in a wide range of serious applications. With this capacity various issues in model determination arise. This research studies the selection of a best model within a collection of such models. It concerns itself with the trade-off between goodness of fit and parsimony and the inappropriateness or shortcomings of customary criteria. The research also addresses the matter of model adequacy. With hierarchical models, model failures can occur at each stage. Approaches for identifying the existence of such failures and their nature are examined by the investigator. Finally, for hierarchical models hyperprior specification is often vague. This work considers conditions under which the resultant posterior is a proper distribution. The modern intellectual contribution of statistics is modeling and inference. In working with scientists from other fields, the statistician helps to formulate appropriate models for the scientists' problems and data as well as to indicate how inference can be developed which provides answers to the questions which motivated the scientists' investigations. With the wide availability of high speed computing, increasingly sophisticated models are being considered permitting the research effort to focus on the determination of the most appropriate model for the application rather than having to settle for an obviously inadequate one. Nonetheless, models must offer some simplification or else they are no easier to understand than the complex phenomenon they are modeling. This research addresses several important issues in the process of determining a satisfying model.