Spike and Slab Models: Theory and Applications

调查人员试图扩大理论和应用的重新标度的尖峰和板模型，一类贝叶斯模型，以解决变量选择和预测的一般问题。 这将在三个不同的目标来实现：（1）通过发展理论以及快速计算算法的非正交设计使用穗和板正交化。 由此产生的预测，一个袋装合奏使用广义岭回归，将被证明具有最先进的预测能力，当一个因素在解释黑箱预测。 有限样本论证形式的理论将表明这是由于选择性收缩，即只有真正为零的系数才向零收缩的性质;（2）通过发展硬阈值估计回归系数的一般方法;（3）通过扩展重新标度的尖峰和板框架以包括非线性模型，诸如广义线性模型和非线性模型，比例生存回归模型与时间依赖的预测。从智力上讲，这项研究将提高我们对模型构建和结果预测的理解，特别是在样本量与预测因子（变量）数量相当或受其支配的不确定环境中。 这种类型的设置在科学设置中变得太普遍了。 其中考虑的应用将是结肠癌基因组学，一个重要的公共卫生问题。 目前，结直肠癌是美国成年人癌症死亡的第二大原因，每年有140，000例新发病例和60，000例死亡。 虽然被广泛使用，但众所周知，目前的分类方案在反映结肠癌行为的实际潜在分子决定因素方面非常不完善。例如，根据目前的临床分期系统，超过20%的癌症转移到肝脏的患者没有接受挽救生命的辅助化疗。 因此，非常需要鉴定将鉴定转移的肿瘤的分子标记。 另一个应用领域将是用于预测冠状动脉搭桥手术后结果的长期预测模型，冠状动脉搭桥手术是阻塞性冠状动脉疾病患者广泛使用的手术方式。 目前的长期预测模型有严重的局限性，阻碍了我们的理解。 另一个应用将是了解心脏和肺移植受体的生存行为以及病毒在移植器官潜在功能障碍中的作用。方法学将通过开发用于在高维设置中快速计算解决方案的软件来补充。

The investigator seeks to expand the theory and application for rescaled spike and slab models, a class of Bayesian models, to address the general problem of variable selection and prediction. This will be accomplished in three distinct aims: (1) By developing theory as well as fast computational algorithms for non-orthogonal designs making using of spike and slab orthogonalization. The resulting predictor, a bagged ensemble derived using generalized ridge regression, will be shown to possess state of the art predictiveness, when one factors in interpretation over black-box prediction. Theory, in the form of finite sample arguments, will show this is due to selective shrinkage, a property whereby only truly zero coefficients are shrunk towards zero; (2) By developing general methodology for hard thresholding estimated regression coefficients; (3) By extending the rescaled spike and slab framework to include non-linear models such as generalized linear models and non-proportional survival regression models with time dependent predictors. Intellectually, this research will enhance our understanding of model building and outcome prediction, especially in ill-determined settings when the sample size is on the order of, or dominated by, the number of predictors (variables). This type of setting is becoming all too common in scientific settings. Among applications considered will be colon cancer genomics, an important public health problem. Currently, colorectal cancer is the second leading cause of cancer mortality in the adult American population, accounting for 140,000 new cases annually and 60,000 deaths. Although widely used, it is known that the current classification scheme is highly imperfect in reflecting the actual underlying molecular determinants of colon cancer behavior. For instance, upwards of 20% of patients whose cancers metastasize to the liver are not given life saving adjuvant chemotherapy based on the current clinical staging system. Thus, there is an important need for the identification of a molecular signature that will identify tumors that metastasize. Another area of application will be long-term prediction models for predicting outcomes following coronary artery bypass surgery, a widely used surgical modality for patients with obstructive coronary artery disease. Current long-term prediction models have serious limitations which have hindered our understanding. Yet another application will be in understanding survival behavior of heart and lung transplant recipients and the role viruses play in potential dysfunction of the transplanted organs. Methodology will be complemented by development of software for fast computational solutions in high dimensional settings.