Advances for Bayesian Model Selection and Inference

该项目将开发新的方法，释放贝叶斯方法的潜力，从当今越来越感兴趣和越来越重要的“大数据”中提取有意义的结构。这将需要创建快速计算的方法，以增强或绕过贝叶斯方法所依赖的速度慢得多的模拟方法。通过更有效地利用高性能计算的能力，我们的方法将为揭示各种科学学科数据中的系统关联提供一个可行的工具。例如：(A)基因组学--确定疾病的遗传决定因素可大大加强有针对性的治疗决定；(B)神经成像--有效的方法将极大地促进理解复杂的大脑结构；(C)环境科学--确定气候变化的决定因素可更好地为政策决策提供信息。这项研究的主旨将是为贝叶斯模型选择和推理的快速确定性搜索实现开发一个广泛的框架。基于EMVS最近开辟的新方向，这项工作将极大地增加大型高维问题的一般贝叶斯实现的可行性。EMVS是一种快速的新的随机搜索替代方案。这将需要开发超越规范正态线性模型的模型类的算法。这些算法的速度将使新的动态后验探索的广泛应用成为可能。我们将研究隐式选择性收缩选择的性质并发展渐近理论。后验重建的新方法将为推断提供新的途径。有效地，该项目将为大型高维问题的后验探索的新范式奠定基础。

This project will develop new approaches that will unleash the potential of Bayesian methods for extracting meaningful structure in the "big data" that are of increasing interest and importance today. This will entail the creation of rapidly computable methods that enhance or bypass the much slower simulation methods upon which Bayesian methods have come to rely. By more efficiently harnessing the power of high-performance computing, our methods will provide a feasible vehicle for uncovering systematic associations in data across a variety of scientific disciplines. Examples include (a) genomics, where identifying the genetic determinants of diseases can substantially enhance targeted therapeutic decisions, (b) neuroimaging, where efficient methods will greatly facilitate understanding the complex brain architecture, and (c) environmental sciences, where identifying the determinants of climate change can better inform policy decisions. The main thrust of this research will be the development of a broad framework for fast deterministic search implementations for Bayesian model selection and inference. Building on new directions recently opened up by EMVS, a fast new alternative to stochastic search, this work will vastly increase the feasibility of general Bayesian implementations for large high-dimensional problems. This will entail the development of algorithms for classes of models that go beyond the canonical normal linear model. The speed of these algorithms will enable the broad application of new dynamic posterior exploration. Properties of the implicit selective shrinkage selection will be studied and asymptotic theory developed. New approaches to posterior reconstruction will provide new avenues for inference. Effectively, this project will lay the groundwork for a new paradigm for posterior exploration in large high-dimensional problems.