Advances in Bayesian Model Choice

研究者考虑了贝叶斯模型选择和线性和广义线性模型平均的新默认先验分布。模型特定参数和先验模型概率的先验选择是至关重要的，特别是在主观规范不切实际或需要“客观”分析的高维关系建模时。研究了具有理想的风险属性、适应未知稀疏度和允许大规模模型搜索计算的新的客观先验族。在高维问题中，模型空间的尺寸是天文数字。开发了用于大规模随机搜索和高维模型空间的模型平均的创新方法和算法，重点是利用图形处理单元（gpu）架构的算法。gpu提供了分布式集群的计算能力，但成本和空间/冷却要求只是它们的一小部分，但在开发利用其架构的统计算法时需要小心。技术的进步导致了高维数据结构的收集，产生了越来越复杂的数据统计模型。数据分析的目标可能包括预测和/或选择模型子集来测试特定理论，或将注意力从许多推测模型减少到几个精心选择的模型；这些都是统计学和所有科学中的基本问题。在这种情况下，模型的不确定性无处不在。贝叶斯方法提供了一种有效的和概念上吸引人的方法，通过贝叶斯模型平均来解决模型的不确定性，结合参数和模型的不确定性，同时仍然允许通过连贯的决策理论原则选择模型。方法的发展是由以下应用产生的问题驱动的：1)确定预测蛋白质活性的重要因素；2)预测国际冲突风险；3)标准污染物对健康的影响；4)确定与卵巢癌风险相关的单核苷酸多态性。由于预测和模型选择是科学和其他领域中最基本和最广泛的问题，该项目的影响超出了上面列出的应用。软件的开发和分发确保了这些方法的广泛可用性。

The investigator considers new default prior distributions forBayesian model selection and model averaging in linear and generalizedlinear models. Prior choice for model specific parameters and forprior model probabilities is of critical importance, particularly formodeling high dimensional relationships where subjectivespecifications are impractical or where an ``objective'' analysis isdesired. New families of objective priors that have desirable riskproperties, adapt to unknown degrees of sparsity, and also permittractable computations for large scale model search are studied. Inhigh dimensional problems, the dimension of the model space isastronomical. Innovative methodology and algorithms for large scalestochastic search and model averaging for high dimensional modelspaces are developed, with an emphasis on algorithms that exploit thearchitecture of Graphical Processing Units (GPUs). GPUs provide thecomputing power of a distributed cluster, but at a fraction of theircost and space/cooling requirements, but require care in thedevelopment of statistical algorithms that take advantage of theirarchitecture.Advances in technology have led to the collection of high dimensionaldata structures, spawning an increasingly complex array of statisticalmodels for data. Goals of data analysis may include prediction and/orselection of a subset of models to test particular theories or toreduce attention from many speculative models to a few well chosenmodels; these are fundamental problems in statistics and throughoutthe sciences. In such settings, model uncertainty is ubiquitous.Bayesian methods offer an effective and conceptually appealingapproach for addressing model uncertainty through Bayesian modelaveraging, incorporating both parameter and model uncertainty, whilestill permitting selection of a model via coherent decision-theoreticprinciples. The methodological developments are driven by issues thatarise from the following applications 1) identifying important factorsto predict protein activity; 2) predicting risk of internationalconflict; 3) health effects of criteria pollutants; and 4) identifyingsingle nucleotide polymorphisms that are associated with ovariancancer risk. As prediction and model selection are some ofthe most fundamental and widespread problems in the sciences andbeyond, the project's impact extends beyond the applications listedabove. The development and distribution of software ensures thatthese methods are widely available.