Scaling up Bayesian Variable Selection for High Dimensions

在生物医学和环境科学的许多应用中，可用数据的复杂性使得统计模型的选择具有挑战性。这个项目的目标是推进基本的科学方法，这将有助于改进使用最先进的贝叶斯方法选择模型。对于具有大量特征的复杂数据，现在例行处理大量相互竞争的模型。对不确定性进行建模的贝叶斯方法为科学中的许多问题提供了自然的解决方案。特别是，将开发贝叶斯框架中模型选择和预测的新算法。这项研究是由从遗传学到气候模型的各种应用推动的。将开发软件并向公众提供，以便新方法易于获得。当特征/预测器的数量很大时，马尔可夫链蒙特卡罗(MCMC)算法经常被用来识别有前途的模型。对于高维问题，这些算法的收敛速度很慢，运行时间也非常长。这个项目致力于开发灵活的贝叶斯变量选择和预测的模型和算法，这些模型和算法可以很好地扩展到高维。线性回归模型的正态误差假设可能并不总是合适的。然而，对于高维数据，当预测因子的数量超过样本量时，这种假设的有效性往往被忽视。在这个项目中，将发展稳健误差分布的贝叶斯变量选择方法，以适应未知程度的尾部重量级和稀疏性。灵活的分级模式将被考虑用于北大西洋热带气旋活动的概率预测。

In many applications in the biomedical and environmental sciences, the complexity of available data makes the selection of statistical models challenging. The goal of this project is to advance basic scientific methodology that will help improve the selection of models using state-of-the-art Bayesian methods. For complex data with a large number of features, it is now routine to entertain an enormous number of competing models. The Bayesian approach to model uncertainty provides a natural solution to many problems in the sciences. In particular, new algorithms for model selection and prediction in a Bayesian framework will be developed. The research is motivated by applications ranging from genetics to climate models. Software will be developed and made publicly available so that the new methods are readily accessible. When the number of features/predictors is large, Markov Chain Monte Carlo (MCMC) algorithms are often used to identify promising models. For high-dimensional problems, these algorithms exhibit slow convergence and have extremely long running times. This project addresses the development of flexible models and algorithms for Bayesian variable selection and prediction that scale well to high dimensions. The assumption of normal errors for the linear regression model may not always be appropriate. However, the validity of this assumption is often overlooked for high-dimensional data, when the number of predictors exceeds the sample size. In this project, Bayesian variable selection methods for robust error distributions will be developed that adapt to unknown degrees of tail heaviness and sparsity. Flexible hierarchical models will be considered for probabilistic prediction of North Atlantic tropical cyclone activity.