Mathematical Sciences: Problems in Hierarchical Model Determination

最近的计算进步使得在广泛的严肃应用中拟合层次模型成为可能。有了这种能力，就会出现模型确定中的各种问题。本研究研究的是在这些模型的集合中选择一个最佳模型。它关注的是合适性和节俭性与习惯标准的不适当性或缺点之间的权衡。该研究还涉及模型充分性问题。使用分层模型，每个阶段都可能出现模型故障。鉴定此类故障的存在及其性质的方法由调查人员进行检查。最后，对于分层模型，超先验规范通常是模糊的。这项工作考虑的条件下，所得后验是一个适当的分布。统计学对现代智力的贡献是建模和推理。在与其他领域的科学家合作时，统计学家帮助为科学家的问题和数据制定适当的模型，并指出如何开发推理，从而为激发科学家调查的问题提供答案。随着高速计算的广泛应用，人们开始考虑越来越复杂的模型，使研究工作能够集中于确定最适合应用程序的模型，而不是不得不满足于一个明显不充分的模型。尽管如此，模型必须提供一些简化，否则它们并不比它们所建模的复杂现象更容易理解。本研究解决了在确定一个令人满意的模型过程中的几个重要问题。

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.