Bayesian variable selection for genetic and genomic studies

高维回归问题中的一个重要问题是，当与数据点数量相比，存在大量潜在预测因子时，回归系数的准确和有效估计。进一步的复杂情况出现在相关预测因子上，导致标准统计模型的推断失效；结果变量的不确定定义，通常是几个不同的可观察特征的不同组成。这类问题的例子出现在基因组学的许多场景中——在确定可能导致某种癌症的基因的表达模式时；在确定哪些基因突变导致某种疾病发生的风险更高时。该项目涉及开发广泛和改进的贝叶斯方法，用于在具有复杂结果的高维回归型问题中进行有效推断，重点是遗传数据应用。此外，我们将把这个框架扩展到各种潜在类模型，并在高维变量选择问题的背景下研究各种先验的操作特征和分析性质。

An important issue in high-dimensional regression problems is the accurate and efficient estimation of regression coefficients when, compared to the number of data points, a substantially larger number of potential predictors are present. Further complications arise with correlated predictors, leading to the breakdown of standard statistical models for inference; and the uncertain definition of the outcome variable, which is often a varying composition of several different observable traits. Examples of such problems arise in many scenarios in genomics- in determining expression patterns of genes that may be responsible for a type of cancer; and in determining which genetic mutations lead to higher risks for occurrence of a disease. This project involves developing broad and improved Bayesian methodologies for efficient inference in high-dimensional regression-type problems with complex outcomes, with a focus on genetic data applications. Further, we will extend this framework to a variety of latent class models, and investigate the operating characteristics and analytical properties of various priors in the context of high-dimensional variable selection problems.