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。 该项目的目标是推进基本的科学方法，这将有助于改善使用最先进的贝叶斯方法的模型选择。对于具有大量特征的复杂数据，处理大量相互竞争的模型现在已成为惯例。贝叶斯模型的不确定性方法为科学中的许多问题提供了一个自然的解决方案。特别是，新的算法模型选择和预测的贝叶斯框架将被开发。这项研究的动机是从遗传学到气候模型的应用。将开发软件并向公众提供，以便随时可以使用新方法。 当特征/预测因子的数量很大时，通常使用马尔可夫链蒙特卡罗（MCMC）算法来识别有希望的模型。对于高维问题，这些算法表现出缓慢的收敛性，并具有非常长的运行时间。 这个项目致力于开发灵活的模型和算法，用于贝叶斯变量选择和预测，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，这种假设的有效性往往被忽视的高维数据，当预测因子的数量超过样本大小。 在这个项目中，贝叶斯变量选择方法的强大的误差分布将开发适应未知程度的尾部沉重和稀疏。 将考虑采用灵活的分层模型对北大西洋热带气旋活动进行概率预测。

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.