Bayesian Formulations for Model Uncertainty

研究者和他的同事考虑了贝叶斯模型选择和模型平均的默认模型不确定性输入规范发展的新方向。针对模型空间先验规范问题，提出了一种可以稀释冗余模型邻域内概率的分布，从而提供了一种更合适的无知表示。针对参数空间先验规范问题，研究了不同先验公式下模型平均的预测性质。特别地，针对先前错误描述的频率后果，开发了新的公式，保持接近极小最大值的行为，预测潜力只有轻微的退化。对于大型数据集的贝叶斯建模，开发了新的自适应公式，以适应局部和全局结构。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。理论最优和实际可行性的目标贯穿始终。本研究的最终目的是增强贝叶斯统计方法在发现和建模大型多变量数据集中变量之间的系统关系方面的潜力。信息技术的爆炸式增长导致这些数据集在商业和科学的广泛不同领域激增。这些方法为改进对许多不同现象的解释和预测提供了一种一般方法，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优区分系统结构的希望，这对于有效挖掘大型详细数据集至关重要。这项研究的主要目的是开发这些方法的自动实现和更丰富的公式，以更充分地利用它们的统计潜力。

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.