Bayesian Formulations for Model Uncertainty

这位研究人员和他的同事们考虑了为贝叶斯模型选择和模型平均制定默认模型不确定性输入规范的新方向。对于模型空间的先验指定问题，提出了在冗余模型的邻域内稀释概率的分布，从而提供了更合适的忽略表示。针对参数空间先验问题，研究了各种先验公式下模型平均的预测性质。特别是，专注于先前错误指定的频率后果，开发了新的公式，这些公式保持了接近极小极大的行为，而预测潜力只有很小的退化。对于大数据集的贝叶斯建模，开发了适应局部和全局结构的新的自适应公式。这包括新的自适应分层建模公式以及用于同时选择模型和数据的新框架。理论上的最优化和实践上的可行性是贯穿始终的目标。这项研究的最终目标是增强贝叶斯统计方法在大型多变量数据集中发现变量之间的系统关系并对其进行建模的潜力。信息技术的爆炸性增长导致这类数据集在商业和科学的广泛不同领域激增。这些方法为改善对许多不同现象的解释和预测提供了一般方法，例如，消费者行为、疾病发病率、金融动荡、工业污染和学校效率。特别是，贝叶斯统计方法提供了从随机噪声中最佳区分系统结构的前景，这对于有效地挖掘大型、详细的数据集至关重要。这项研究的主旨是开发这些方法的自动实施和更丰富的公式，以便更充分地开发它们的统计潜力。

The investigator and his colleagues consider new directions for the development of default model uncertainty input specifications for Bayesian model selection and model averaging. For the problem of model space prior specification, distributions are developed that dilute probability within neighborhoods of redundant models, thereby providing a more appropriate representation of ignorance. For the problem of parameter space prior specification, the predictive properties of model averaging are investigated for various prior formulations. In particular, focusing on the frequentist consequences of prior misspecification, new formulations are developed that maintain near-minimax behavior with only a minor degradation of predictive potential. For Bayesian modeling of large data sets, new adaptive formulations are developed that accommodate local as well as global structure. This includes new adaptive hierarchical modeling formulations as well as a new framework for simultaneous model and data selection. The goals of theoretical optimality and practical feasibility are considered throughout. The ultimate objective of this research is to enhance the potential of Bayesian statistical methods for discovering and modeling systematic relationships between variables in large multi-variable data sets. The explosive growth of information technologies has led to the proliferation of such data sets across widely diverse fields in business and science. Such methods offer a general approach towards improving explanations and predictions of many varied phenomenon such as, for example, consumer behavior, disease incidence, financial turbulence, industrial pollution and school efficiency. Bayesian statistical methods, in particular, offer the promise of optimally distinguishing systematic structure from random noise, which is of critical importance for effective mining of large, detailed data sets. The main thrust of this research is on the development of automatic implementations and richer formulations of these methods that will more fully exploit their statistical potential.