Advances in Bayesian Model Choice

研究者考虑了线性和广义线性模型中贝叶斯模型选择和模型平均的新默认先验分布。 事先选择模型的具体参数和forprior模型的概率是至关重要的，特别是formodeling高维关系的主观specifications是不切实际的，或在“客观”的分析是理想的。 新的家庭的客观先验，具有理想的riskproperties，适应未知程度的稀疏性，也可用于大规模模型搜索计算进行了研究。在高维问题中，模型空间的维数是天文数字。针对高维模型空间的大规模随机搜索和模型平均，提出了创新的方法和算法，重点研究了利用图形处理单元（GPU）结构的算法。 GPU提供了分布式集群的计算能力，但其成本和空间/冷却需求却只有分布式集群的一小部分，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模型阵列。数据分析的目标可能包括预测和/或选择模型的子集来测试特定的理论或将注意力从许多投机模型减少到少数精心选择的模型;这些都是统计学和整个科学的基本问题。在这种情况下，模型的不确定性是无处不在的。贝叶斯方法提供了一个有效的和概念上appealingapproach解决模型的不确定性，通过贝叶斯modelaveraging，将参数和模型的不确定性，同时仍然允许选择一个模型通过连贯的decision-theoreticprinciples。 方法学的发展是由以下应用中出现的问题驱动的：1）识别预测蛋白质活性的重要因素; 2）预测国际冲突的风险; 3）标准污染物的健康影响; 4）识别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普遍的问题，该项目的影响超出了上述应用范围。 软件的开发和发行确保了这些方法的广泛应用。

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.