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，在“大数据”中提取有意义的结构，这是今天越来越感兴趣和重要的。 这将需要创建快速可计算的方法，增强或绕过贝叶斯方法所依赖的慢得多的模拟方法。 通过更有效地利用高性能计算的力量，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种可行的工具。例子包括：（a）基因组学，确定疾病的遗传决定因素可以大大加强有针对性的治疗决定;（B）神经成像，有效的方法将大大有助于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以更好地为政策决定提供信息。 这项研究的主要目标是发展一个广泛的框架，快速确定性搜索实现贝叶斯模型选择和推理。 基于EMVS最近开辟的新方向，这是随机搜索的一种快速新选择，这项工作将大大提高大型高维问题的一般贝叶斯实现的可行性。这将需要为超越规范正态线性模型的模型类开发算法。这些算法的速度将使新的动态后验探索的广泛应用。隐式选择收缩选择的性质将被研究和渐近理论的发展。后路重建的新方法将为推断提供新的途径。 有效地，这个项目将奠定一个新的范例后探索在大型高维问题的基础。

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.